Recent ucimath items

Rational points on a family of genus 3 hyperelliptic curves

Tue, 26 May 2026 00:00:00 +0000

We compute the rational points on certain members of the following family of hyperelliptic curves C a : y 2 = x 8 + ( 4 − 4 a 4 ) x 6 + ( 8 a 4 + 6 ) x 4 + ( 4 − 4 a 4 ) x 2 + 1 via the method first developed by Dem'yanenko [Dem68] and then further generalized by Manin [Man69]. In particular, we show that the method of Chabauty–Coleman, while applicable to certain members of this family, is not the most efficient way of computing C a ( Q ) . We adapt the approach of [Kul99], incorporating root numbers to further restrict the possible ranks of the elliptic curves arising in the Jacobian decomposition.

Hippocampal ensembles represent sequential relationships among discrete nonspatial events

Thu, 7 May 2026 00:00:00 +0000

ABSTRACT The hippocampus is critical to the temporal organization of our experiences, including the ability to remember past event sequences and predict future ones. Although this fundamental capacity is conserved across modalities and species, its underlying neuronal mechanisms remain poorly understood. Here we recorded hippocampal ensemble activity as rats remembered a sequence of nonspatial events (5 odor presentations unfolding over several seconds), using a task with established parallels in humans. Using novel statistical methods and deep learning techniques, we then identified new forms of sequential organization in hippocampal activity linked with task performance. We discovered that sequential firing fields (“time cells”) provided temporal information within and across events in the sequence, and that distinct types of task-critical information (stimulus identity, temporal order, and trial outcome) were also sequentially differentiated within event presentations. Finally,...

Optimal Transport based Cross-Domain Integration for Heterogeneous Data

Thu, 7 May 2026 00:00:00 +0000

Detecting dynamic patterns shared across heterogeneous datasets is a critical yet challenging task in many scientific domains, particularly within the biomedical sciences. Systematic heterogeneity inherent in diverse data sources can significantly hinder the effectiveness of existing machine learning methods in uncovering shared underlying dynamics. Additionally, practical and technical constraints in real-world experimental designs often limit data collection to only a small number of subjects, even when rich, time-dependent measurements are available for each individual. These limited sample sizes further diminish the power to detect common dynamic patterns across subjects. In this article, we propose a novel heterogeneous data integration framework based on optimal transport to extract shared patterns in the conditional mean dynamics of target responses. The key advantage of the proposed method is its ability to enhance discriminative power by reducing heterogeneity unrelated...

Some Banach Spaces Congruent To Their Conjugates

Fri, 3 Apr 2026 00:00:00 +0000

Mazur remarked that there are separable infinite dimensional Banach spaces which are congruent (i.e. isometrically isomorphic) with their conjugates [1; page 245]. I am not aware of the reference to the example (s) Mazur had in mind. In [3; page 195] the term " self-conjugate space " is introduced but not defined, it merely being noted that L2(0, 1) is self-conjugate because it is congruent to its conjugate and that (notation from this point follows [2]) l2 and Z2 n are also self-conjugate.

Solution of Games by Computer

Fri, 3 Apr 2026 00:00:00 +0000

Computational and mathematical features of several games (the term is used in a broad sense) are analyzed. The games include Blackjack, Baccarat, Go, and the stock market. A simple point count method for measuring favorable expectations in Blackjack is discussed. A proof is outlined of the fact that there are no currently practical methods for winning in the various forms of Baccarat. Precise formulations of the colloquial rules for Go are presented. Small board games (up to 1 X8, 2 X4, 3X3) are solved completely, but even 1 X9 remains unknown! Certain easily verified patterns in stock market price and volume series are indicated.

Trefftzs Award: The Capital Growth Model: An Empirical Investigation

Fri, 3 Apr 2026 00:00:00 +0000

Modern micro-capital theory offers three major alternative choice theoretic approaches from which a set of market equilibrium prices can be derived. These approaches are:

1. Time-state preference theory of Arrow (1] and Debreu (6],

2. The capital asset pricing model (hereafter CAPM) of Sharpe (34], Lintner (23], and Fama (7],

3. The capital growth model of Kelly (16], Breiman (5], and Latane (17].1

Of the three approaches, time-state preference theory is probably the most eloquent and robust theoretical approach to normative portfolio and capital market theory inasmuch as it is "capable of being shifted comfortably between individual and market levels of analysis, between perfect and imperfect markets, and between conditions of certainty and uncertainty with the fundamental theoretical elements exhibiting a continuity and a clarity otherwise unattainable."2 Also, this theory is intuitively appealing because of its consistency with the multi-period consumption-investment...

Finite Dimensional Normed Spaces

Fri, 3 Apr 2026 00:00:00 +0000

Several characterisations of finite dimensional normed spaces are wellknown. The usual characterisation is some variant of the theorem of F. Riesz [1; Theorem IV 3.5].

A normed linear space is finite dimensional if and only if its closed unit sphere is compact. Numerous additional conditions may be given. For example, it is well known (see, e.g. [4; p. 190, Ex. 1, and p. 193, Ex. 1])that a normed linear space is finite dimensional if and only if its conjugate is finite dimensional. Another condition is that a normed linear space is finite dimensional if and only if every linear functional is continuous. The proof is straightforward. We give below two characterisations which we believe are new.

The Relation Between a Compact Linear Operator and its Conjugate

Fri, 3 Apr 2026 00:00:00 +0000

Introduction. We present a systematic account of known theorems relating compact linear operators and their conjugates. Examples are given showing that all the theorems which are "possible" in a certain broad sense are already known. The general method is that of [6].

Poincaré's conjecture and the distribution of digits in tables

Fri, 3 Apr 2026 00:00:00 +0000

Let Ei(n) be the number of even digits and Oi(n) the number of odd digits occurring in the ith column of the table of logarithms of the first n integers to the base 10. In 1899 Henri Poincaré [3, page 193 ] expressed the belief that limn Ei(n)/n and limn Oi(n)/n exist and equal 2. Poincaré provided mathematical support for this conjecture in [2]. Franel [1 ] disproved Poincaré’s conjecture by showing that these limits do not exist. Franel also showed that the sequence of arithmetic means of the digits in the ith column has no limit, and gave information on the set of accumulation points of these sequences.

Internal Points of Convex Sets

Fri, 3 Apr 2026 00:00:00 +0000

An interior point of a set K in a topological linear space is always an internal point of the set [1; V, 2.1 (b)], as follows immediately from the definitions. Klee gives an example [3; p. 450] which shows that the converse may fail for certain subspaces of the lp spaces, even though the set K is convex. It is the purpose of this note to describe as best we can the class of topological linear spaces for which the converse fails. We show that it fails for a large class of infinite dimensional topological linear spaces. The class includes all normed linear spaces and even all pre-F-spaces. Notation and terminology follow [1] unless otherwise indicated. If A is a set, card A designates the cardinality of A.

Preface: Introduction to the Classic Papers and Theories

Fri, 3 Apr 2026 00:00:00 +0000

In this part of the book, we present papers that formalize, generalize, and extend the early results on the Kelly strategy. Although the early papers on the Kelly optimal growth strategy contained powerful results, the topic was not significant in mainstream financial economics. Unfortunately, despite lots of good evidence, it is still not a serious part of academic financial economics. Roll (1973), for example, shows that in his data set, capital growth and mean-variance portfolios are similar. Thorp (1971) had shown that the Kelly strategies were not necessarily mean-variance efficient and Markowitz (1976) argued that the Kelly strategy was the limiting mean-variance portfolio. These papers appear later in this book. Here we take up the work of those who extended the early results and begin to consider the good and bad properties of these strategies and the sensitivity of the results to data inputs and errors.

MultiGrid Preconditioners for Mixed Finite Element Methods of the Vector Laplacian

Fri, 3 Apr 2026 00:00:00 +0000

Due to the indefiniteness and poor spectral properties, the discretized linear algebraic system of the vector Laplacian by mixed finite element methods is hard to solve. A block diagonal preconditioner has been developed and shown to be an effective preconditioner by Arnold et al. (Acta Numer 15:1–155, 2006). The purpose of this paper is to propose alternative and effective block diagonal and approximate block factorization preconditioners for solving these saddle point systems. A variable V-cycle multigrid method with the standard point-wise Gauss–Seidel smoother is proved to be a good preconditioner for the discrete vector Laplacian operator. The major benefit of our approach is that the point-wise Gauss–Seidel smoother is more algebraic and can be easily implemented as a black-box smoother. This multigrid solver will be further used to build preconditioners for the saddle point systems of the vector Laplacian. Furthermore it is shown that Maxwell’s equations with the divergent...

E1578: A Divergent Series

Fri, 3 Apr 2026 00:00:00 +0000

Consider the ∑^∞ _n-1| sin n | ^a, where a is an arbitrary positive number. For which values of a does the series converge and for which values does it diverge?

The probability that a matrix has a saddle point

Fri, 3 Apr 2026 00:00:00 +0000

Given a "randomly selected" m X n matrix, the probability that it has a saddle point is m!n!/(m+n-1)!.

Best possible triangle inequalities for statistical metric spaces

Fri, 3 Apr 2026 00:00:00 +0000

A statistical metric space (briefly, an SM space) is a set S and a mapping Ӻ from S X S into the set of distribution functions (i.e., real-valued functions of a real variable which are everywhere defined, nondecreasing, left-continuous and have inf 0 and sup 1). The distribution function Ӻ:(p, q) associated with a pair of points (p, q) in S is denoted by F_pq .

The Range as Range Space for Compact Operators. II.

Fri, 3 Apr 2026 00:00:00 +0000

If X and Y are normed linear spaces and T : X à Y is a compact operator, when does T_o : X à R(T) is the range of T and T_o is defined by T_oX = Tx, remain (or fail to remain) compact? We extend the answers given in [5] to this question.

Note on Linear Operators.

Fri, 3 Apr 2026 00:00:00 +0000

Introduction. This note answers two questions. 1.) If X and Y are Banach spaces, with Y inseparable, does it ever happen that all the bounded operators from X into Y are compact? 2.) If X and Y are Banach spaces, consider the following subset of the space of bounded operators from X into Y with the uniform topology: the operators (compact operators) with both a) non-dense range in Y, and b) which send some non-zero vector into zero. Does this subset of operators (compact operators) ever have an interior point?

A Favorable Side Bet in Nevada Baccarat

Fri, 3 Apr 2026 00:00:00 +0000

A winning strategy is developed for the nine to one side bet on a Banker natural nine. Let n be the number of cards that remain for play. Let t be the number of nines that remain for play. If p(n, t) is the probability of a natural nine when n and t are given, then p(n, t) is greater than 0.1 frequently enough to make the counting of n and t the basis for a practical winning strategy. The Kelly criterion (pIay to maximize the expected value of the log of capital) is used to determine bet sizes for favorable situations. Similar strategies are developed for the side bets on Banker natural eight, Player natural nine, and Player natural eight. The relationships between the four side bets are analyzed. I t is shown that the main (roughly 1 : 1) bets on Banker and Player occasionally favor the player. There are theoretical favorable strategies...

A partial analysis of Go

Fri, 3 Apr 2026 00:00:00 +0000

A game called Computer Go is defined. Computer Go differs from the game of Japanese Go only in that certain imprecisely defined conventions have been replaced by precise rules. Some general theorems on Computer Go are given, as well as a scheme for analysing the game with the aid of a computer. Several reduced versions of Computer Go were analysed, and the resultant strategies are briefly described.

Operator representation theorems

Fri, 3 Apr 2026 00:00:00 +0000

We consider representations of bounded, compact and weakly compact linear operators from a Banach space to a space BC(S), where S is an arbitrary topological space and BC(S) is the space of bounded continuous scalar-valued functions on S with the sup norm. With the use of our theorems, one can quickly and easily deduce numerous operator representation theorems, many of which are new. For example, taking as domain space a space with a well-known conjugate space and range space as either co or m, one fills in quite a few blanks in Tables VI A, B and C in [4]. Our proofs for range BC(S), S arbitrary, are appreciably simpler than those found in the literature for range C(S), S a compact Hausdorff space.

Repeated Independent Trials and a Class of Dice Problems

Fri, 3 Apr 2026 00:00:00 +0000

This discussion was originally motivated by a class of dice problems. They are illustrated by the following examples, which will be referred to in the sequel. Assume that two true dice are rolled repeatedly.

Problem 1. Find the probability that both the totals 5 and 9 appear before a 7 appears.

Problem 2. Find the probability that both the totals 4 and 6 appear before a 7 appears.

Problem 3. Find the probability that 4, 5, 6, 8, 9, 10 all appear before 7 appears.

Problem 4. Find the probability that all totals different from 7 appear before a 7 appears.

On some open questions concerning strictly singular operators

Fri, 3 Apr 2026 00:00:00 +0000

Kato introduces the following concept of a strictly singular operator in [3].

Definition. Let X and Y be Banach spaces and let T be a bounded linear operator mapping X into F. T is said to be strictly singular if given any infinite dimensional subspace M of X, T restricted to M is not an isomorphism (i.e., linear homeomorphism).

In particular, every compact operator is strictly singular. Kato proceeds to show that the space S of strictly singular operators possesses some of the important features of the space of compact operators, e.g., S is a closed subspace of the space of bounded linear operators from X to Y. If X= Y, then S is a closed ideal. If X and Y are Hubert spaces, then every strictly singular operator from X to Y is compact.

The following two questions, posed by Kato, are answered below.

(1)...

A Favorable Strategy for Twenty-One

Fri, 3 Apr 2026 00:00:00 +0000

Introduction.- It has long been an open question as to whether those of the standard gambling games which are not repeated independent trials admit strategies favorable^† to the player. There have been numerous implications^2-4that favorable strategies do not exist. In this note, we settle the issue by showing that there is a markedly favorable mathematical^‡ strategy for one of the most widely played games, twenty-one, or blackjack.

Book Review: The Theory of Blackjack

Fri, 3 Apr 2026 00:00:00 +0000

The Theory of Blackjack is a fundamental contribution to our understanding of this game. It is also unusually well written and amusing. This book is for readers having some familiarity with blackjack and blackjack card counting systems. Those who don't can browse in the references for adequate background.

Projections onto the subspace of compact operators

Fri, 3 Apr 2026 00:00:00 +0000

Introduction. The purpose of this paper is to establish the following theorem.

Multigrid Methods for Constrained Minimization Problems and Application to Saddle Point Problems

Fri, 3 Apr 2026 00:00:00 +0000

The first order condition of the constrained minimization problem leads to a saddle point problem. A multigrid method using a multiplicative Schwarz smoother for saddle point problems can thus be interpreted as a successive subspace optimization method based on a multilevel decomposition of the constraint space. Convergence theory is developed for successive subspace optimization methods based on two assumptions on the space decomposition: stable decomposition and strengthened Cauchy-Schwarz inequality, and successfully applied to the saddle point systems arising from mixed finite element methods for Poisson and Stokes equations. Uniform convergence is obtained without the full regularity assumption of the underlying partial differential equations. As a byproduct, a V-cycle multigrid method for non-conforming finite elements is developed and proved to be uniform convergent with even one smoothing step.

Symplectic Morse theory and Witten deformation

Wed, 25 Mar 2026 00:00:00 +0000

On symplectic manifolds, we introduce a Morse-type complex with elements generated by pairs of critical points of a Morse function. The differential of the complex consists of gradient flows and an integration of the symplectic structure over spaces of gradient flow lines. Using results from the Witten deformation method, we prove that the cohomology of this complex is independent of both the Riemannian metric and the Morse function used to define the complex and is in fact isomorphic to the cohomology of differential forms of Tsai, Tseng and Yau (TTY). We also obtain Morse-type inequalities that bound the dimensions of the TTY cohomologies by the number of Morse critical points and the interaction of symplectic structure with the critical points.

The Eilenberg-Borsuk duality theorem for metric spaces

Tue, 24 Mar 2026 00:00:00 +0000

The Eilenberg-Borsuk duality theorem for metric spaces

A Note on Nonfinitely Generated Projective Zπ-Modules

Thu, 19 Mar 2026 00:00:00 +0000

A Note on Nonfinitely Generated Projective Zπ-Modules

Partially Bounded Sets of Infinite Width

Thu, 19 Mar 2026 00:00:00 +0000

A closed convex subset A of a real Banach space X (I) has finite width if A lies between two closed parallel hyperplanes (2) A has finite width in the direction x ≠ O if there is a constant w_x such that every line parallel to x intersects A in an interval of length no more than w_x, and (3) A is partially bounded (by K) if there is a finite least upper bound K for the radii of spheres contained in A. In answer to questions of Clark (J. London Math. Soc. 43 (1968), 513-516) we show: Theorem. For every infinite dimensional Banach space with separable infinite dimensional quotient, and every K > 0 there is a closed convex body of infinite width which is partially bounded by K. Theorem. Every Banach space with an infinite dimensional separable quotient has a closed convex body which is partially bounded but not of finite width in any direction. Theorem. Every Banach space having an infinite dimensional quotient space with a Schauder basis has a closed convex...

Spatial and temporal evaluations of the liquid argon purity in ProtoDUNE-SP

Mon, 16 Mar 2026 00:00:00 +0000

Liquid argon time projection chambers (LArTPCs) rely on highly pure argon to ensure that ionization electrons produced by charged particles reach readout arrays. ProtoDUNE Single-Phase (ProtoDUNE-SP) was an approximately 700-ton liquid argon detector intended to prototype the Deep Underground Neutrino Experiment (DUNE) Far Detector Horizontal Drift module. It contains two drift volumes bisected by the cathode plane assembly, which is biased to create an almost uniform electric field in both volumes. The DUNE Far Detector modules must have robust cryogenic systems capable of filtering argon and supplying the TPC with clean liquid. This paper will explore comparisons of the argon purity measured by the purity monitors with those measured using muons in the TPC from October 2018 to November 2018. A new method is introduced to measure the liquid argon purity in the TPC using muons crossing both drift volumes of ProtoDUNE-SP. For extended periods on the timescale of weeks, the drift...

Mapping cone and Morse theory

Wed, 25 Feb 2026 00:00:00 +0000

Mapping cone and Morse theory

Idempotent ideals in integral group rings II

Tue, 24 Feb 2026 00:00:00 +0000

Let π be a finite group and let Zπ be its integral group ring. In a recent paper [1], the author investigated the following problem. Determine-which finite groups π have the property that Zπ be without non-trivial idempotent ideals (two-sided). It was proved that, if π is nilpotent then Zπ has no non-trivial idempotent ideals. Also, if π is not solvable then there is a non-trivial idempotent ideal (contained in the augmentation ideal) of Zπ. The remaining case where π is solvable but not nilpotent is still unresolved. We conjectured that the complete solution to the problem was precisely the solvable groups.

Minimal ring extensions of the integers exhibiting Kochen–Specker contextuality

Tue, 24 Feb 2026 00:00:00 +0000

This paper is a contribution to the algebraic study of contextuality in quantum theory. As an algebraic analogue of Kochen and Specker’s no-hidden-variables result, we investigate rational subrings over which the partial ring of [Formula: see text] symmetric matrices ([Formula: see text]) admits no morphism to a nonzero commutative ring, which we view as an “algebraic hidden state”. For [Formula: see text], the minimal such ring is shown to be [Formula: see text], while for [Formula: see text] the minimal subring is [Formula: see text] itself. The proofs rely on the construction of new sets of integer vectors in dimensions 3 and 6 that have no Kochen–Specker coloring.

Generalized Topologies for Statistical Metric Spaces

Tue, 24 Feb 2026 00:00:00 +0000

Introduction. Statistical metric spaces, introduced by K. Menger in [5], are a generalization of metric spaces in which distances are given by distribution functions rather than by numbers (1). Just as with metric spaces, there is no a priori topology. But whereas metric spaces have a single natural topology, there are many structures, satisfying some or all of the axioms of a to1>ology, that may be associated with a statistical metric space in a natural way. One such structure for statistical metric spaces was introduced by B. Schweizer and .A. Sklar in [7] (2).

The invention of the first wearable computer

Mon, 23 Feb 2026 00:00:00 +0000

The first wearable computer was conceived in 1955 by the author to predict roulette, culminating in a joint effort at M.I.T. with Claude Shannon in 1960-61. The final operating version was tested in Shannon’s basement home lab in June of 1961. The cigarette pack sized analog device yielded an expected gain of +44% when betting on the most favored “octant.”The Shannons and Thorps tested the computer in Las Vegas in the summer of 1961. The predictions there were consistent with the laboratory expected gain of 44% but a minor hardware problem deferred sustained serious betting.We kept the method and the existence of the computer secret until 1966.

Immersions of Metric Spaces into Euclidean Spaces

Mon, 23 Feb 2026 00:00:00 +0000

Introduction. In a recent paper on isotopy invariants (1), S. T. Hu defined the enveloping space Em(X) of any given topological space X for each integer ra > 1. By an application of the Smith theory to the singular cohomology of the enveloping space Em{X), he obtained his immersion classes ̀Ψ_m ⁿ(X) for every n = 1, 2, 3, . . . and proved (3) the main theorem that a necessary condition for a compact metric space X to be immersible into then-dimensional Euclidean space Rⁿ is Ψ₂ ⁿ(X) = 0. This theorem was proved earlier by W. T. Wu (4) for finitely triangulable spaces X using purely combinatorial methods.

The objective of the present paper is to prove the above-mentioned theorem for arbitrary metric spaces. Our treatment follows that of S. T. Hu (3) in which he considers a homotopically equivalent subspace of E_m(X). By a further...

The Fundamental Theorem of Card Counting with applications to Trente-et-Quarante and Baccarat

Mon, 23 Feb 2026 00:00:00 +0000

The Fundamental Theorem of Card Counting is a unifying principle for the analysis of card games of chance which are characterized by sampling without replacement. The Theorem says (roughly) the "spread" in distribution of player expectations for partially depleted card packs increases with depletion of the card pack. Furthermore, average player expectation is non-decreasing (increasing under suitable hypotheses) with increasing depletion.

The Theorem is used to prove that significant favorable strategies based on card counting do not exist for Trente-et-Quarante or for "tie" bets in Nevada Baccarat, This is in sharp contrast with previous results for Blackjack and for Nevada Baccarat side bets on natural eight and natural nine.

Nonrandom Shuffling with Applications to the Game of Faro

Mon, 23 Feb 2026 00:00:00 +0000

De Moivre, Euler, and Montmort analyzed a predecessor of Faro. We consider the modern game first under the assumption of random shuffling, then with nonrandom shuffling. With random shuffling we find the house edge can be less than 0.0006 percent, but it is at least 0.526 percent if the player is limited to negative expectation bets. Human shuffling is nonrandom and a simple model for it indicates that, in principle, the player can achieve significant positive expectation. The ideas used to apply nonrandom shuffling to Far0 also extend to other games. We illustrate with casino Blackjack. An appendix discusses previous work on modern Faro.

Idempotent ideals in integral group rings

Mon, 23 Feb 2026 00:00:00 +0000

Let π be a finite group and let Zπ be its integral group ring. A well-known result of Swan [5, Corollary 8.11 states that Zπ has no nontrivial idempotent elements. It follows by a proof in [7, p. 2151 that if π is abelian, then Zπ. has no nontrivial idempotent ideals. On the other hand, if π is perfect (and hence not solvable), then the augmentation ideal of Zπ is idempotent [2, p. 1901. The following natural problem is considered here. Determine which finite groups π have the property that Zπ be without nontrivial idempotent ideals.

A Computer Assisted Study of Go on M x N Boards

Mon, 23 Feb 2026 00:00:00 +0000

The game of Go invites analysis. The rules seem few and simple, suggesting that the game may have helpful theorems. Tens of millions of people play and skill has developed over centuries to extraordinary levels. Thus, computer analysis can be tested against analysis by highly skilled human players.

We study M x N boards, rather than the usual 19 x 19. We begin with the computer-assisted complete tree calculation for the tiniest boards. The analysis extends to slightly larger boards with the aid of various lemmas and concepts of connectedness and symmetry. The usual rules are incomplete. Though difficulties rarely arise from this on a 19 x 19 board, they are frequent on small boards. We therefore extend and complete the rules in a way which, we believe, preserves their spirit.

We give bounds on the value of the game and on its combinatorial magnitude. We discuss a heuristic strategy based on potential. The flow chart for our computer program is included and may be...

Partially bounded sets of infinite width.

Mon, 23 Feb 2026 00:00:00 +0000

Clark [2] introduces those notions for a convex subset A of a real Banach space X: (t) A has finite width if A lies between two closed parallel hyperplanes, i. e. if there is a contininuous linear functional x* on X and two real numbers α and β with α < x* (x) < β for all x in A, (2) A has finite width in the direction x =I= 0 if there is a constant w_x such that every line parallel to x intersects A in an interval of length no more than w_x, i. e. if α x + y and β x+ y belong to A then I β - α I < w_x, and (3) A is partially bounded (hy K) if there is a finite least upper bound K for the radii of spheres contained in A. In what follows, we...

Solution of a poker variant

Mon, 23 Feb 2026 00:00:00 +0000

In one variation on poker, each player is dealt one card which he places exposed onhis forehead. Thus each player knows every other hand but does not see his own. Wecall this variation "inverse poker". We show that, under certain restrictions, two-personinverse poker and two-person ordinary poker are isomorphic games. In particular, the existing solutions to two-person poker variants all yield solutions to two-person inverse poker variants.

The metrization of statistical metric spaces

Mon, 23 Feb 2026 00:00:00 +0000

In a previous paper on statistical metric spaces [3] it was shownthat a statistical metric induces a natural topology for the space on which it is defined and that with this topology a large class of statistical metric (briefly, SM) spaces are Hausdorff spaces.In this paper we show that this result (Theorem 7.2 of [3]) can be considerably generalized. In addition, as an immediate corollary of this generalization, we prove that with the given topology a large number of SM spaces are metrizable, i.e., that in numerous instances the existence of a statistical metric implies the existence of an ordinary metric.

The strong maximum modulus theorem for analytic functions into a Banach space

Mon, 23 Feb 2026 00:00:00 +0000

Let D be a domain (an open connected subset) in the complex plane and let be a complex-valued analytic function on D. Then the classical maximum modulus theorem says that either (z) has no maximum on D or that | ∫ (z) | is a constant on D. If | ∫ (z) | is a constant, it follows readily that | ∫ (z) | is itself constant.

If ∫ has values in a complex β -space, it is well known [5, p. 230], or [6, p. 100] that the theorem holds. However, the strong form of the maximum modulus theorem, where if ∫ (z)| is constant then /(z) is constant, is no longer true in general. This is illustrated by the following simple example [6, p. 100]. Let D be the open unit disc and define ∫: D —> ∫² _oo by ∫ (z) = (1, z). Then/is analytic, not constant, and | ∫ (z) | = 1 for all z in D. (Notation throughout this paper, such as ∫² _oo , follows [5] wherever...

Risk arbitrage in the Nikkei put warrant market of 1989-1990

Wed, 18 Feb 2026 00:00:00 +0000

This paper discusses the Nikkei put warrant market in Toronto and New York during 1989-1990. Three classes of long term American puts were traded which when evaluated in yen are ordinary, product and exchange asset puts, respectively. Type I do not involve exchange rates for yen investors. Type 11, called quantos, fix in advance the exchange rate to be used on expiry in the home currency. Type 111 evaluate the strike and spot prices of the Nikkei Stock Average in the home currency rather than in yen. For typically observed parameters, type I are theoretically more valuable than type I1 which in turn are more valuable than type 111. In late 1989 and early 1990 there were significant departures from fair values in various markets. This was a market with a set of complex financial instruments that even sophisticated investors needed time to learn about to price properly. Investors in Canada were willing to buy puts at far more than fair value based on historical volatility. In addition,...

Options on Commodity Forward Contracts

Wed, 18 Feb 2026 00:00:00 +0000

We develop formulas for "European" options on commodity forward contracts. The assumptions and derivations are simple. The qualitative behavior of the formulas is developed for an intuitive overview. The put formula and related ideas were applied to successfully manage a quarter billion dollar hedge of GNMA futures versus standbys.

Long-term capital growth: the good and bad properties of the Kelly and fractional Kelly capital growth criteria

Wed, 18 Feb 2026 00:00:00 +0000

The main advantage of the Kelly criterion, which maximizes the expected value of the logarithm of wealth period by period, is that it maximizes the limiting exponential growth rate of wealth. The main disadvantage of the Kelly criterion is that its suggested wagers may be very large because the Arrow–Pratt risk aversion, the reciprocal of current wealth, is small compared with other commonly chosen utility functions. Hence, the Kelly criterion is relatively risky in the short term. And although most of the time Kelly bettors will have a lot of final wealth after a long sequence of favorable bets, it is possible, through bad scenarios, to lose most of one's wealth. Hence, care in the use of Kelly and fractional Kelly strategies is crucial.

How Does the Fortune's Formula Kelly Capital Growth Model Perform?

Wed, 18 Feb 2026 00:00:00 +0000

William Poundstone’s book, Fortune’s Formula, brought the Kelly capital growth criterion to the attention of investors. But how do full and fractional Kelly strategies perform in practice? The authors study three simple investment situations and simulate the behavior of these strategies over medium-term horizons using a large number of scenarios. The results show 1) the great superiority of full Kelly and close-to-full Kelly strategies over longer horizons in that they earn very large gains a large fraction of the time, 2) the very risky short-term performance of Kelly and high-fractional Kelly strategies, 3) a consistent trade-off of growth versus security as a function of the bet size determined by the various strategies, and 4) no matter how favorable the investment opportunities are, or how long the finite horizon is, a sequence of bad scenarios can lead to very poor final wealth outcomes with a loss of most of the investor’s initial capital. Hence, in practice, financial...

The Kelly Criterion and the Stock Market

Wed, 18 Feb 2026 00:00:00 +0000

The purpose of this expository note is to describe the Kelly criterion, a theory of optimal resource apportionment during favorable gambling games, with special attention to an application in the U.S. stock market.

By a "favorable game" we mean one in which there exists a strategy such that Pr(lim_{n --> ∞} X_n = +∞) > 0, where X_n is the player's capital after n trials. We shall first discuss the case of discrete binomial gambling games and then extend the discussion to continuous gambling games.

Attempt at a Strongest Vector Topology

Tue, 17 Feb 2026 00:00:00 +0000

A set A in E is circled if aA CA for all scalars a such that I a I ~ 1. A set is radial at O if it contains a line segment through O in each direction. A vector topology for E is a topology such that addition and scalar multiplication are each jointly continuous. A local base is a fundamental system of neighborhoods of 0.

Analysis of yeast's ORF upstream regions by parallel processing, microarrays, and computational methods.

Wed, 28 Jan 2026 00:00:00 +0000

We use a network of workstations to compute all pairwise alignments of the 500 bp upstream regions of 6,225 yeast ORFs (Open Reading Frames). We correlate the alignments with DNA microarray expression data from budding yeast cells over an oxidative stress time course. We confirm on a genomic scale that, in general, genes with extremely similar upstream regions have similar activity levels, even when located on different chromosomes. As the difference in upstream regions increases, the correlation rapidly drops towards zero. Divergent ORFs with overlapping upstream regions do not seem to be correlated in any way. The pairwise alignments coupled with the expression data, together with other computational techniques, suggest a few new putative regulatory binding sites that can be tested experimentally. Finally, we investigate the inherent symmetry present in the two strands of the yeast genome. We show that it extends at least all the way up to 9-mers and is likely to result from...

A Goldbach theorem for Laurent series semidomains

Wed, 5 Nov 2025 00:00:00 +0000

A Goldbach theorem for Laurent series semidomains

Efficient mathematical methodology to determine multistep mutant burden in spatially growing cell populations

Tue, 30 Sep 2025 00:00:00 +0000

The accurate computational prediction of mutant burden in spatially structured growing cell populations is a major goal both for basic evolutionary science, such as interpreting bacterial evolution studies, and for clinical applications, such as predicting the timing of drug resistance-induced cancer relapse for individual patients. Yet, this is currently not feasible for biologically realistic parameters, due to the inefficiency of computationally simulating stochastic mutant dynamics in large populations. Here, we fill this gap by deriving universal scaling laws that allow the straightforward prediction of the number of single-hit, double-hit, and multihit mutants as a function of wild-type population size in spatially expanding populations, in different spatial geometries, without the need to perform lengthy computer simulations. We demonstrate the applicability of this approach by reconciling different results from experimental evolution studies in bacteria that examine the...

Dual Coalgebras of Twisted Tensor Products

Wed, 10 Sep 2025 00:00:00 +0000

We investigate cases where the finite dual coalgebra of a twisted tensor product of two algebras is a cotwisted tensor product of their respective finite dual coalgebras. This is achieved by interpreting the finite dual as a topological dual; in order to prove this, we show that the continuous dual is a strong monoidal functor on linearly topologized vector spaces whose open subspaces have finite codimension. We describe a sufficient condition for the result on finite dual coalgebras to be applied, and we specialize this condition to particular constructions including Ore extensions, smash product algebras, and bitwisted tensor products of bialgebras.

Regulation of feather length: FGF/IGF signaling and NOTCH/YAP modulation of progenitor cell topology

Fri, 29 Aug 2025 00:00:00 +0000

The regulation of organ size is a fundamental biological question. This study investigates how feather length is regulated in chickens. We found that collar bulge stem cell zones vary in size: main sickle > lesser sickle > contour feathers. During growth, IGF and FGF9 signaling are highly expressed, while BMP, WIF1, and FGF18 increase toward growth termination. Functional assays show that insulin-like growth factor/fibroblast growth factor signaling promotes feather elongation via tyrosine kinase receptor signaling. Single-cell RNA sequencing analysis reveals accelerated differentiation of keratinocytes in short contour feathers compared to long sickle feathers. In Phoenix chickens, superlong main sickle feathers exhibit specialized stem cell zones with enhanced DLL1 expression and expanded intermediate-layer cell clusters with dynamic interactions involving NOTCH1/DLL1, YAP1, and WNT signaling in progenitor...

Supernova pointing capabilities of DUNE

Fri, 15 Aug 2025 00:00:00 +0000

The determination of the direction of a stellar core collapse via its neutrino emission is crucial for the identification of the progenitor for a multimessenger follow-up. A highly effective method of reconstructing supernova directions within the Deep Underground Neutrino Experiment (DUNE) is introduced. The supernova neutrino pointing resolution is studied by simulating and reconstructing electron-neutrino charged-current absorption on and elastic scattering of neutrinos on electrons. Procedures to reconstruct individual interactions, including a newly developed technique called “brems flipping,” as well as the burst direction from an ensemble of interactions are described. Performance of the burst direction reconstruction is evaluated for supernovae happening at a distance of 10 kpc for a specific supernova burst flux model. The pointing resolution is found to be 3.4 degrees at 68% coverage for a perfect interaction-channel classification and a fiducial mass of 40 kton,...

Second-Order Effects of Chemotherapy Pharmacodynamics and Pharmacokinetics on Tumor Regression and Cachexia

Fri, 8 Aug 2025 00:00:00 +0000

Drug dose response curves are ubiquitous in cancer biology, but these curves are often used to measure differential response in first-order effects: the effectiveness of increasing the cumulative dose delivered. In contrast, second-order effects (the variance of drug dose) are often ignored. Knowledge of second-order effects may improve the design of chemotherapy scheduling protocols, leading to improvements in tumor response without changing the total dose delivered. By considering treatment schedules with identical cumulative dose delivered, we characterize differential treatment outcomes resulting from high variance schedules (e.g. high dose, low dose) and low variance schedules (constant dose). We extend a previous framework used to quantify second-order effects, known as antifragility theory, to investigate the role of drug pharmacokinetics. Using a simple one-compartment model, we find that high variance schedules are effective for a wide range of cumulative dose values....

Uncovering minimal pathways in melanoma initiation

Tue, 5 Aug 2025 00:00:00 +0000

Melanomas are genetically heterogeneous, displaying mitogen-activated protein kinase mutations and homozygous loss of tumor suppressor genes. Mouse models combining such mutations produce fast-growing tumors. In contrast, rare, slow-growing tumors arise in mice combining Braf activation with heterozygous loss of Pten. Here we show that similar tumors can arise in albino mice bearing only a Braf mutation. Incidence kinetics suggest a stochastic event underlies tumorigenesis in tumors that arise with only a Braf mutation, yet de novo mutations or structural variants that could explain the incidence of most tumors could not be found. Single-cell transcriptomics of tumors identify a cell type resembling “neural crest-like” cells in human and mouse melanomas. These exist in normal mouse skin, expand upon Braf activation, and persist through serial transplantation; analyses of gene expression suggest they serve as precursors of malignant cells. This state may serve as an intermediate...

The track-length extension fitting algorithm for energy measurement of interacting particles in liquid argon TPCs and its performance with ProtoDUNE-SP data

Fri, 25 Jul 2025 00:00:00 +0000

This paper introduces a novel track-length extension fitting algorithm for measuring the kinetic energies of inelastically interacting particles in liquid argon time projection chambers (LArTPCs). The algorithm finds the most probable offset in track length for a track-like object by comparing the measured ionization density as a function of position with a theoretical prediction of the energy loss as a function of the energy, including models of electron recombination and detector response. The algorithm can be used to measure the energies of particles that interact before they stop, such as charged pions that are absorbed by argon nuclei. The algorithm's energy measurement resolutions and fractional biases are presented as functions of particle kinetic energy and number of track hits using samples of stopping secondary charged pions in data collected by the ProtoDUNE-SP detector, and also in a detailed simulation. Additional studies describe the impact of the dE/dx model on...

Revisiting Murray’s Law in Pulmonary Arteries: Exploring branching patterns and principles

Fri, 20 Jun 2025 00:00:00 +0000

In 1926, Cecil D. Murray published a fundamental law of physiology relating the form and function of branched vessels. Murray's Law predicts that the diameter of a parent vessel branching into two child branches is mathematically related by a cube law based on parabolic flow and power minimization with vascular volume. This law is foundational for computational analyses of branching vascular structures. However, pulmonary arteries exhibit morphometric and hemodynamic characteristics that may deviate from classical predictions. This study investigates the morphometry of pulmonary arterial networks, examining relationships between parent and child vessel diameters across species. We analyzed three-dimensional segmentations of pulmonary arterial geometries from healthy subjects across four species: human (n = 7), canine (n = 5), swine (n = 4), and murine (n = 3). Our findings reveal an average exponent value of 2.31(±0.60) in human, 2.13(±0.54) in canine, 2.10(±0.49) in swine, and...

In-vivo optical microscopy and single cell transcriptomics approaches provide insights into therapeutic response of vitiligo

Wed, 18 Jun 2025 00:00:00 +0000

In-vivo optical microscopy and single cell transcriptomics approaches provide insights into therapeutic response of vitiligo

Full event particle-level unfolding with variable-length latent variational diffusion

Thu, 22 May 2025 00:00:00 +0000

SciPost Journals Publication Detail SciPost Phys. 18, 117 (2025) Full event particle-level unfolding with variable-length latent variational diffusion

Categories of hypermagmas, hypergroups, and related hyperstructures

Wed, 7 May 2025 00:00:00 +0000

In order to diagnose the cause of some defects in the category of canonical hypergroups, we investigate several categories of hyperstructures that generalize hypergroups. By allowing hyperoperations with possibly empty products, one obtains categories with desirable features such as completeness and cocompleteness, free functors, regularity, and closed monoidal structures. We show by counterexamples that such constructions cannot be carried out within the category of canonical hypergroups. This suggests that (commutative) unital, reversible hypermagmas—which we call mosaics—form a worthwhile generalization of (canonical) hypergroups from the categorical perspective. Notably, mosaics contain pointed simple matroids as a subcategory, and projective geometries as a full subcategory.

A Novel Stochastic Interacting Particle-Field Algorithm for 3D Parabolic-Parabolic Keller-Segel Chemotaxis System

Wed, 23 Apr 2025 00:00:00 +0000

Abstract: We introduce an efficient stochastic interacting particle-field (SIPF) algorithm with no history dependence for computing aggregation patterns and near singular solutions of parabolic-parabolic Keller-Segel (KS) chemotaxis system in three-dimensional (3D) space. In our algorithm, the KS solutions are approximated as empirical measures of particles coupled with a smoother field (concentration of chemo-attractant) variable computed by a spectral method. Instead of using heat kernels that cause history dependence and high memory cost, we leverage the implicit Euler discretization to derive a one-step recursion in time for stochastic particle positions and the field variable based on the explicit Green’s function of an elliptic operator of the form Laplacian minus a positive constant. In numerical experiments, we observe that the resulting SIPF algorithm is convergent and self-adaptive to the high-gradient part of solutions. Despite the lack of analytical knowledge...

FWin Transformer for Dengue Prediction Under Climate and Ocean Influence

Wed, 23 Apr 2025 00:00:00 +0000

Dengue fever is one of the most deadly mosquito-born tropical infectious diseases. Detailed long range forecast model is vital in controlling the spread of disease and making mitigation efforts. In this study, we examine methods used to forecast dengue cases for long range predictions. The dataset consists of local climate/weather in addition to global climate indicators of Singapore from 2000 to 2019. We utilize newly developed deep neural networks to learn the intricate relationship between the features. The baseline models in this study are in the class of recent transformers for long sequence forecasting tasks. We found that a Fourier mixed window attention (FWin) based transformer performed the best in terms of both the mean square error and the maximum absolute error on the long range dengue forecast up to 60 weeks.

A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller–Segel chemotaxis systems

Wed, 23 Apr 2025 00:00:00 +0000

A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller–Segel chemotaxis systems

Computing effective diffusivities in 3D time-dependent chaotic flows with a convergent Lagrangian numerical method

Wed, 23 Apr 2025 00:00:00 +0000

In this paper, we study the convergence analysis for a robust stochastic structure-preserving Lagrangian numerical scheme in computing effective diffusivity of time-dependent chaotic flows, which are modeled by stochastic differential equations (SDEs). Our numerical scheme is based on a splitting method to solve the corresponding SDEs in which the deterministic subproblem is discretized using a structure-preserving scheme while the random subproblem is discretized using the Euler-Maruyama scheme. We obtain a sharp and uniform-in-time convergence analysis for the proposed numerical scheme that allows us to accurately compute long-time solutions of the SDEs. As such, we can compute the effective diffusivity for time-dependent chaotic flows. Finally, we present numerical results to demonstrate the accuracy and efficiency of the proposed method in computing effective diffusivity for the time-dependent Arnold-Beltrami-Childress (ABC) flow and Kolmogorov flow in three-dimensional space.

DeepParticle: Learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method

Wed, 23 Apr 2025 00:00:00 +0000

DeepParticle: Learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method

Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

Wed, 23 Apr 2025 00:00:00 +0000

We prove, under mild conditions, the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model, both in batch gradient descent and stochastic gradient descent. We also discuss a Riemannian version of the Adam algorithm. We show numerical simulations of these algorithms on various benchmarks.

AFIDAF: Alternating Fourier and Image Domain Adaptive Filters as an Efficient Alternative to Attention in ViTs

Wed, 23 Apr 2025 00:00:00 +0000

We propose and demonstrate an alternating Fourier and image domain filtering approach for feature extraction as an efficient alternative to build a vision backbone without using the computationally intensive attention. The performance among the lightweight models reaches the state-of-the-art level on ImageNet-1K classification, and improves downstream tasks on object detection and segmentation consistently as well. Our approach also serves as a new tool to compress vision transformers (ViTs).

Existence of an Effective Burning Velocity in a Cellular Flow for the Curvature G-Equation Proved Using a Game Analysis

Wed, 23 Apr 2025 00:00:00 +0000

G-equation is a popular level set model in turbulent combustion, and becomes an advective mean curvature type evolution equation when curvature of a moving flame in a fluid flow is considered: Gt+(1-ddiv(DG|DG|))+|DG|+V(x)·DG=0. Here d> 0 is the Markstein number and the positive part () + is imposed to avoid a non-physical negative laminar flame speed. For simplicity of presentation, we focus mainly on the case when V: R2→ R2 is the two dimensional cellular flow with Hamiltonian H=sinx1sinx2 and amplitude A. Our main result is that for any unit vector p∈ R2 , there exists a positive number H¯ (p) such that if G(x, 0) = p· x , then |G(x,t)-p·x+H¯(p)t|≤CinR2×[0,∞) for a constant C depending only on on the Markstein number d and the cellular flow amplitude A. The number H¯ (p) corresponds to the effective burning velocity in the physics literature. The non-coercivity encountered here is one of the major difficulties for homogenization of the mean curvature-type equations. To overcome...

An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation

Wed, 23 Apr 2025 00:00:00 +0000

An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation

Bifurcation of homogenization and nonhomogenization of the curvature G-equation with shear flows

Wed, 23 Apr 2025 00:00:00 +0000

The level-set curvature G-equation, a well-known model in turbulent combustion, has the following form (Formula presented.) Here the cutoff correction ()+ is imposed to avoid non-physical negative local burning velocity. The existence of the effective burning velocity has been established for a large class of physically relevant incompressible flows V in two dimensions [13] via game theory dynamics. In this paper, we show that the effective burning velocity associated with shear flows in dimensions three or higher ceases to exist when the flow intensity surpasses a bifurcation point. The characterization of the bifurcation point in three dimensions is closely related to the regularity theory of two-dimensional minimal surface type equations due to [31]. As a consequence, a bifurcation also exists for the validity of full homogenization of the curvature G-equation associated with shear flows.

Lagrangian, game theoretic, and PDE methods for averaging G-equations in turbulent combustion: existence and beyond

Wed, 23 Apr 2025 00:00:00 +0000

G-equations are popular level set Hamilton–Jacobi nonlinear partial differential equations (PDEs) of first or second order arising in turbulent combustion. Characterizing the effective burning velocity (also known as the turbulent burning velocity) is a fundamental problem there. We review relevant studies of the G-equation models with a focus on both the existence of effective burning velocity (homogenization), and its dependence on physical and geometric parameters (flow intensity and curvature effect) through representative examples. The corresponding physical background is also presented to provide motivations for mathematical problems of interest. The lack of coercivity of Hamiltonian is a hallmark of G-equations. When either the curvature of the level set or the strain effect of fluid flows is accounted for, the Hamiltonian becomes highly nonconvex and nonlinear. In the absence of coercivity and convexity, the PDE (Eulerian) approach suffers from insufficient compactness...

An augmented subspace based adaptive proper orthogonal decomposition method for time dependent partial differential equations

Wed, 23 Apr 2025 00:00:00 +0000

An augmented subspace based adaptive proper orthogonal decomposition method for time dependent partial differential equations

An Image Segmentation Model with Transformed Total Variation

Wed, 23 Apr 2025 00:00:00 +0000

An Image Segmentation Model with Transformed Total Variation

“If I can’t help, I find someone who can”: Lower-SES Latine parents’ adaptive responses to math support challenges

Wed, 23 Apr 2025 00:00:00 +0000

Latine parents from lower socioeconomic backgrounds in the United States (US) often face challenges when supporting their adolescents’ education in subjects like math. Guided by strengths-based, culturally grounded frameworks, this study explored the challenges Latine parents faced when supporting adolescents’ math learning and how they leveraged their community cultural wealth via specific strategies to address challenges. We conducted semi-structured qualitative interviews with 20 Latine-descent parents (19 mothers, one father; 12 with less than a high school education, five with a high school education, three with some college education) of adolescents (eight girls, 12 boys; eight 6th graders, seven 7th graders, and five 8th graders) attending four middle schools in southern California. Systematic coding and theming of the interview data were used to help identify challenges parents experienced at the individual level (e.g., gaps in content/curriculum knowledge, problems with...

RETHINKING THE BENEFITS OF STEERABLE FEATURES IN 3D EQUIVARIANT GRAPH NEURAL NETWORKS

Wed, 23 Apr 2025 00:00:00 +0000

Theoretical and empirical comparisons have been made to assess the expressive power and performance of invariant and equivariant GNNs. However, there is currently no theoretical result comparing the expressive power of k-hop invariant GNNs and equivariant GNNs. Additionally, little is understood about whether the performance of equivariant GNNs, employing steerable features up to type-L, increases as L grows - especially when the feature dimension is held constant. In this study, we introduce a key lemma that allows us to analyze steerable features by examining their corresponding invariant features. The lemma facilitates us in understanding the limitations of k-hop invariant GNNs, which fail to capture the global geometric structure due to the loss of geometric information between local structures. Furthermore, we analyze the ability of steerable features to carry information by studying their corresponding invariant features. In particular, we establish that when the input spatial...

Interruption of the intratumor CD8+ T cell:Treg crosstalk improves the efficacy of PD-1 immunotherapy

Mon, 7 Apr 2025 00:00:00 +0000

PD-1 blockade unleashes potent antitumor activity in CD8⁺ T cells but can also promote immunosuppressive T regulatory (Treg) cells, which may worsen the response to immunotherapy. Tumor-Treg inhibition is a promising strategy to improve the efficacy of checkpoint blockade immunotherapy; however, our understanding of the mechanisms supporting tumor-Tregs during PD-1 immunotherapy is incomplete. Here, we show that PD-1 blockade increases tumor-Tregs in mouse models of melanoma and metastatic melanoma patients. Mechanistically, Treg accumulation is not caused by Treg-intrinsic inhibition of PD-1 signaling but depends on an indirect effect of activated CD8⁺ T cells. CD8⁺ T cells produce IL-2 and colocalize with Tregs in mouse and human melanomas. IL-2 upregulates the anti-apoptotic protein ICOS on tumor-Tregs, promoting their accumulation. Inhibition of ICOS signaling before PD-1 immunotherapy improves control over immunogenic melanoma....

Post-transfusion activation of coagulation pathways during severe COVID-19 correlates with COVID-19 convalescent plasma antibody profiles

Fri, 4 Apr 2025 00:00:00 +0000

Early antibody therapy can prevent severe SARS-CoV-2 infection (COVID-19). However, the effectiveness of COVID-19 convalescent plasma (CCP) therapy in treating severe COVID-19 remains inconclusive. To test a hypothesis that some CCP units are associated with a coagulopathy hazard in severe disease that offsets its benefits, we tracked 304 CCP units administered to 414 hospitalized COVID-19 patients to assess their association with the onset of unfavorable post-transfusion D-dimer trends. CCP recipients with increasing or persistently elevated D-dimer trajectories after transfusion experienced higher mortality than those whose D-dimer levels were persistently low or decreasing after transfusion. Within the CCP donor-recipient network, recipients with increasing or persistently high D-dimer trajectories were skewed toward association with a minority of CCP units. In in vitro assays, CCP from "higher-risk" units had higher cross-reactivity with the spike protein of human seasonal...

Dynamically adjusted cell fate decisions and resilience to mutant invasion during steady-state hematopoiesis revealed by an experimentally parameterized mathematical model

Tue, 1 Apr 2025 00:00:00 +0000

A major next step in hematopoietic stem cell (HSC) biology is to enhance our quantitative understanding of cellular and evolutionary dynamics involved in undisturbed hematopoiesis. Mathematical models have been and continue to be key in this respect, and are most powerful when parameterized experimentally and containing sufficient biological complexity. In this paper, we use data from label propagation experiments in mice to parameterize a mathematical model of hematopoiesis that includes homeostatic control mechanisms as well as clonal evolution. We find that nonlinear feedback control can drastically change the interpretation of kinetic estimates at homeostasis. This suggests that short-term HSC and multipotent progenitors can dynamically adjust to sustain themselves temporarily in the absence of long-term HSCs, even if they differentiate more often than they self-renew in undisturbed homeostasis. Additionally, the presence of feedback control in the model renders the system...

Leveraging gene correlations in single cell transcriptomic data

Mon, 3 Mar 2025 00:00:00 +0000

BACKGROUND: Many approaches have been developed to overcome technical noise in single cell RNA-sequencing (scRNAseq). As researchers dig deeper into data-looking for rare cell types, subtleties of cell states, and details of gene regulatory networks-there is a growing need for algorithms with controllable accuracy and fewer ad hoc parameters and thresholds. Impeding this goal is the fact that an appropriate null distribution for scRNAseq cannot simply be extracted from data when ground truth about biological variation is unknown (i.e., usually). RESULTS: We approach this problem analytically, assuming that scRNAseq data reflect only cell heterogeneity (what we seek to characterize), transcriptional noise (temporal fluctuations randomly distributed across cells), and sampling error (i.e., Poisson noise). We analyze scRNAseq data without normalization-a step that skews distributions, particularly for sparse data-and calculate p-values associated with key statistics....

Chemically Informed Deep Learning for Interpretable Radical Reaction Prediction

Sat, 1 Mar 2025 00:00:00 +0000

Organic radical reactions are crucial in many areas of chemistry, including synthetic, biological, and atmospheric chemistry. We develop a predictive framework based on the interaction of molecular orbitals that operates on mechanistic-level radical reactions. Given our chemistry-aware model, all predictions are provided with different levels of interpretability. Our models are trained and evaluated using the RMechDB database of radical reaction steps. Our model predicts the correct orbital interaction and products for 96% of the test reactions in RMechDB. By chaining these predictions, we perform a pathway search capable of identifying all intermediates and byproducts of a radical reaction. We test the pathway search on two classes of problems in atmospheric and polymerization chemistry. RMechRP is publicly available online at https://deeprxn.ics.uci.edu/rmechrp/.

Barcoded HIV-1 reveals viral persistence driven by clonal proliferation and distinct epigenetic patterns

Sat, 22 Feb 2025 00:00:00 +0000

The HIV reservoir consists of infected cells in which the HIV-1 genome persists as provirus despite effective antiretroviral therapy (ART). Studies exploring HIV cure therapies often measure intact proviral DNA levels, time to rebound after ART interruption, or ex vivo stimulation assays of latently infected cells. This study utilizes barcoded HIV to analyze the reservoir in humanized mice. Using bulk PCR and deep sequencing methodologies, we retrieve 890 viral RNA barcodes and 504 proviral barcodes linked to 15,305 integration sites at the single RNA or DNA molecule in vivo. We track viral genetic diversity throughout early infection, ART, and rebound. The proviral reservoir retains genetic diversity despite cellular clonal proliferation and viral seeding by rebounding virus. Non-proliferated cell clones are likely the result of elimination of proviruses associated with transcriptional activation and viremia. Elimination of proviruses associated with viremia is less prominent...

A Tour of Noncommutative Spectral Theories

Wed, 12 Feb 2025 00:00:00 +0000

A Tour of Noncommutative Spectral Theories

First measurement of the total inelastic cross section of positively charged kaons on argon at energies between 5.0 and 7.5 GeV

Tue, 4 Feb 2025 00:00:00 +0000

ProtoDUNE Single-Phase (ProtoDUNE-SP) is a 770-ton liquid argon time projection chamber that operated in a hadron test beam at the CERN Neutrino Platform in 2018. We present a measurement of the total inelastic cross section of charged kaons on argon as a function of kaon energy using 6 and beam momentum settings. The flux-weighted average of the extracted inelastic cross section at each beam momentum setting was measured to be for the setting and for the setting. Published by the American Physical Society 2024

Single-cell transcriptomics of human-skin-equivalent organoids

Sat, 1 Feb 2025 00:00:00 +0000

Several methods for generating human-skin-equivalent (HSE) organoid cultures are in use to study skin biology; however, few studies thoroughly characterize these systems. To fill this gap, we use single-cell transcriptomics to compare in vitro HSEs, xenograft HSEs, and in vivo epidermis. By combining differential gene expression, pseudotime analyses, and spatial localization, we reconstruct HSE keratinocyte differentiation trajectories that recapitulate known in vivo epidermal differentiation pathways and show that HSEs contain major in vivo cellular states. However, HSEs also develop unique keratinocyte states, an expanded basal stem cell program, and disrupted terminal differentiation. Cell-cell communication modeling shows aberrant epithelial-to-mesenchymal transition (EMT)-associated signaling pathways that alter upon epidermal growth factor (EGF) supplementation. Last, xenograft HSEs at early time points post transplantation significantly rescue many in vitro...

Superstable lipid vacuoles endow cartilage with its shape and biomechanics

Wed, 29 Jan 2025 00:00:00 +0000

Conventionally, the size, shape, and biomechanics of cartilages are determined by their voluminous extracellular matrix. By contrast, we found that multiple murine cartilages consist of lipid-filled cells called lipochondrocytes. Despite resembling adipocytes, lipochondrocytes were molecularly distinct and produced lipids exclusively through de novo lipogenesis. Consequently, lipochondrocytes grew uniform lipid droplets that resisted systemic lipid surges and did not enlarge upon obesity. Lipochondrocytes also lacked lipid mobilization factors, which enabled exceptional vacuole stability and protected cartilage from shrinking upon starvation. Lipid droplets modulated lipocartilage biomechanics by decreasing the tissue's stiffness, strength, and resilience. Lipochondrocytes were found in multiple mammals, including humans, but not in nonmammalian tetrapods. Thus, analogous to bubble wrap, superstable lipid vacuoles confer skeletal tissue with cartilage-like properties without "packing...

Surface remodeling and inversion of cell-matrix interactions underlie community recognition and dispersal in Vibrio cholerae biofilms

Mon, 20 Jan 2025 00:00:00 +0000

Biofilms are ubiquitous surface-associated bacterial communities embedded in an extracellular matrix. It is commonly assumed that biofilm cells are glued together by the matrix; however, how the specific biochemistry of matrix components affects the cell-matrix interactions and how these interactions vary during biofilm growth remain unclear. Here, we investigate cell-matrix interactions in Vibrio cholerae, the causative agent of cholera. We combine genetics, microscopy, simulations, and biochemical analyses to show that V. cholerae cells are not attracted to the main matrix component (Vibrio polysaccharide, VPS), but can be attached to each other and to the VPS network through surface-associated VPS and crosslinks formed by the protein Bap1. Downregulation of VPS production and surface trimming by the polysaccharide lyase RbmB cause surface remodeling as biofilms age, shifting the nature of cell-matrix interactions from attractive to repulsive and facilitating cell...

Essential dimension via prismatic cohomology

Wed, 15 Jan 2025 00:00:00 +0000

Essential dimension via prismatic cohomology

Detecting global and local hierarchical structures in cell-cell communication using CrossChat

Fri, 20 Dec 2024 00:00:00 +0000

Cell-cell communication (CCC) occurs across different biological scales, ranging from interactions between large groups of cells to interactions between individual cells, forming a hierarchical structure. Globally, CCC may exist between clusters or only subgroups of a cluster with varying size, while locally, a group of cells as sender or receiver may exhibit distinct signaling properties. Current existing methods infer CCC from single-cell RNA-seq or Spatial Transcriptomics only between predefined cell groups, neglecting the existing hierarchical structure within CCC that are determined by signaling molecules, in particular, ligands and receptors. Here, we develop CrossChat, a novel computational framework designed to infer and analyze the hierarchical cell-cell communication structures using two complementary approaches: a global hierarchical structure using a multi-resolution clustering method, and multiple local hierarchical structures using a tree detection method. This framework...

Inferring Stochastic Rates from Heterogeneous Snapshots of Particle Positions

Sat, 7 Dec 2024 00:00:00 +0000

Many imaging techniques for biological systems—like fixation of cells coupled with fluorescence microscopy—provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of...

Tipping points in epithelial-mesenchymal lineages from single-cell transcriptomics data

Mon, 11 Nov 2024 00:00:00 +0000

Understanding cell fate decision-making during complex biological processes is an open challenge that is now aided by high-resolution single-cell sequencing technologies. Specifically, it remains challenging to identify and characterize transition states corresponding to "tipping points" whereby cells commit to new cell states. Here, we present a computational method that takes advantage of single-cell transcriptomics data to infer the stability and gene regulatory networks (GRNs) along cell lineages. Our method uses the unspliced and spliced counts from single-cell RNA sequencing data and cell ordering along lineage trajectories to train an RNA splicing multivariate model, from which cell-state stability along the lineage is inferred based on spectral analysis of the model's Jacobian matrix. Moreover, the model infers the RNA cross-species interactions resulting in GRNs and their variation along the cell lineage. When applied to epithelial-mesenchymal transition in ovarian and...

Single-cell transcriptomics reveals aberrant skin-resident cell populations and identifies fibroblasts as a determinant in rosacea

Fri, 8 Nov 2024 00:00:00 +0000

Rosacea is a chronic inflammatory skin disorder, whose underlying cellular and molecular mechanisms remain obscure. Here, we generate a single-cell atlas of facial skin from female rosacea patients and healthy individuals. Among keratinocytes, a subpopulation characterized by IFNγ-mediated barrier function damage is found to be unique to rosacea lesions. Blocking IFNγ signaling alleviates rosacea-like phenotypes and skin barrier damage in mice. The papulopustular rosacea is featured by expansion of pro-inflammatory fibroblasts, Schwann, endothelial and macrophage/dendritic cells. The frequencies of type 1/17 and skin-resident memory T cells are increased, and vascular mural cells are characterized by activation of inflammatory pathways and impaired muscle contraction function in rosacea. Most importantly, fibroblasts are identified as the leading cell type producing pro-inflammatory and vasodilative signals in rosacea. Depletion of fibroblasts or knockdown of PTGDS, a gene specifically...

Inferring pattern-driving intercellular flows from single-cell and spatial transcriptomics

Thu, 7 Nov 2024 00:00:00 +0000

From single-cell RNA-sequencing (scRNA-seq) and spatial transcriptomics (ST), one can extract high-dimensional gene expression patterns that can be described by intercellular communication networks or decoupled gene modules. These two descriptions of information flow are often assumed to occur independently. However, intercellular communication drives directed flows of information that are mediated by intracellular gene modules, in turn triggering outflows of other signals. Methodologies to describe such intercellular flows are lacking. We present FlowSig, a method that infers communication-driven intercellular flows from scRNA-seq or ST data using graphical causal modeling and conditional independence. We benchmark FlowSig using newly generated experimental cortical organoid data and synthetic data generated from mathematical modeling. We demonstrate FlowSig’s utility by applying it to various studies, showing that FlowSig can capture stimulation-induced changes to paracrine...

Circadian cilia transcriptome in mouse brain across physiological and pathological states

Tue, 5 Nov 2024 00:00:00 +0000

Primary cilia are dynamic sensory organelles that continuously undergo structural modifications in response to environmental and cellular signals, many of which exhibit rhythmic patterns. Building on our previous findings of rhythmic cilia-related gene expression in diurnal primates (baboon), this study extends the investigation to the nocturnal mouse brain to identify circadian patterns of cilia gene expression across brain regions. We used computational techniques and transcriptomic data from four publicly available databases, to examine the circadian expression of cilia-associated genes within six brain areas: brainstem, cerebellum, hippocampus, hypothalamus, striatum, and suprachiasmatic nucleus. Our analysis reveals that a substantial proportion of cilia transcripts exhibit circadian rhythmicity across the examined regions, with notable overrepresentation in the striatum, hippocampus, and cerebellum. We also demonstrate region-specific variations in the abundance and timing...

Large‐scale analysis reveals spatiotemporal circadian patterns of cilia transcriptomes in the primate brain

Fri, 1 Nov 2024 00:00:00 +0000

Cilia are dynamic subcellular systems, with core structural and functional components operating in a highly coordinated manner. Since many environmental stimuli sensed by cilia are circadian in nature, it is reasonable to speculate that genes encoding cilia structural and functional components follow rhythmic circadian patterns of expression. Using computational methods and the largest spatiotemporal gene expression atlas of primates, we identified and analyzed the circadian rhythmic expression of cilia genes across 22 primate brain areas. We found that around 73% of cilia transcripts exhibited circadian rhythmicity across at least one of 22 brain regions. In 12 brain regions, cilia transcriptomes were significantly enriched with circadian oscillating transcripts, as compared to the rest of the transcriptome. The phase of the cilia circadian transcripts deviated from the phase of the majority of the background circadian transcripts, and transcripts coding for cilia basal body...

The Generalized Continuum Hypothesis Can Fail Everywhere

Tue, 22 Oct 2024 00:00:00 +0000

The Generalized Continuum Hypothesis Can Fail Everywhere

Descent for n-bundles

Wed, 9 Oct 2024 00:00:00 +0000

Descent for n-bundles