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With the recent advancements in machine learning (ML), artificial neural networks (ANN) are starting to play an increasingly important role in quantitative finance. Dynamic portfolio optimization is among many problems that have significantly benefited from a wider adoption of deep learning (DL). While most existing research has primarily focused on how DL can alleviate the curse of dimensionality when solving the Hamilton-Jacobi-Bellman (HJB) equation, some very recent developments propose to forego derivation and solution of HJB in favor of empirical utility maximization over dynamic allocation strategies expressed through ANN. In addition to being simple and transparent, this approach is universally applicable, as it is essentially agnostic about market dynamics. To showcase the method, we apply it to optimal portfolio allocation between a cash account and the S&P 500 index modeled using geometric Brownian motion or the Heston model. In both cases, the results are demonstrated to be on par with those under the theoretical optimal weights assuming isoelastic utility and real-time rebalancing. A set of R codes for a broad class of stochastic volatility models are provided as a supplement., Comment: 14 pages, 5 figures

Background/Objectives: Cataract surgery, a very common and critical procedure for restoring vision, has outcomes that can vary based on patient demographics. This study aimed to elucidate the effects of age and sex on the risk factors, intraoperative complications, and postoperative outcomes of cataract surgery. Subjects/Methods: Conducted as a single-center retrospective cohort study, it analyzed 691 eyes from 589 individuals who underwent surgery at a tertiary referral center, utilizing data from electronic medical records to assess preoperative risk factors, intraoperative complications, and pre- and post-operative best corrected visual acuity (BCVA) along with demographic data. Results: The main results highlighted that males aged 65-75 years exhibited significantly higher rates of functional postoperative BCVA (91% for males vs. 79% for females, p=0.007), a disparity that is not explained by differences in surgical complications or risk factor prevalence. Furthermore, the study identified age-specific thresholds where BCVA improvements significantly declined beyond 65 years for females and 75 years for males. The likelihood of worsened BCVA post-surgery increased with age for both sexes, with a significant decline in BCVA improvement transitioning from 55-65 years to 65-75 years age groups. Conclusions: The findings underscore the critical influence of both sex and age on cataract surgery outcomes, revealing significant sex-specific age thresholds that signal lesser improvements in postoperative BCVA. These insights advocate for the integration of patient age and sex into preoperative evaluations to better tailor the timing and planning of cataract surgery, ultimately aiming to optimize clinical outcomes.

Quantization has established itself as the primary approach for decreasing the computational and storage expenses associated with Large Language Models (LLMs) inference. The majority of current research emphasizes quantizing weights and activations to enable low-bit general-matrix-multiply (GEMM) operations, with the remaining non-linear operations executed at higher precision. In our study, we discovered that following the application of these techniques, the primary bottleneck in LLMs inference lies in the softmax layer. The softmax operation comprises three phases: exponent calculation, accumulation, and normalization, Our work focuses on optimizing the first two phases. We propose an analytical approach to determine the optimal clipping value for the input to the softmax function, enabling sub-4-bit quantization for LLMs inference. This method accelerates the calculations of both $e^x$ and $\sum(e^x)$ with minimal to no accuracy degradation. For example, in LLaMA1-30B, we achieve baseline performance with 2-bit quantization on the well-known "Physical Interaction: Question Answering" (PIQA) dataset evaluation. This ultra-low bit quantization allows, for the first time, an acceleration of approximately 4x in the accumulation phase. The combination of accelerating both $e^x$ and $\sum(e^x)$ results in a 36.9% acceleration in the softmax operation.

We present foundations of globally valued fields, i.e., of a class of fields with an extra structure, capturing some aspects of the geometry of global fields, based on the product formula. We provide a dictionary between various data defining such extra structure: syntactic (models of some unbounded continuous logic theory), Arakelov theoretic, and measure theoretic. In particular we obtain a representation theorem relating globally valued fields and adelic curves defined by Chen and Moriwaki., Comment: 51 pages

This study uses Program for the International Assessment of Adult Competencies (PIAAC) data to examine latent profiles of engagement in reading, numeracy, writing, and computer skills-use for U.S. adults with low literacy skills. Additionally, we examine how these profiles relate to overall literacy performance and demographic heterogeneity. Results indicate five engagement profiles: High (8%), Average-High (44%), Average-Low (40%), and two generally Low profiles that are most differentiated on numeracy skills-use engagement (5.5%, 2%). High and Average-High engagement profiles had higher probabilities of adults scoring at a higher literacy level than the Average-Low profile and to a greater degree than the lowest engagement profile. Covariates of learning disability status, English speaker status, race, ethnicity, age, and educational attainment were also related to differences in literacy performance and skills-use engagement. Employment status was unrelated to differences in literacy performance and skills-use engagement. Generally, native English speakers, non-learning disabled adults, younger adults, those identifying as non-Hispanic and White, and adults with higher educational attainment (high school/some college and college degree or higher) had higher probabilities of higher literacy performance, particularly in the High and Average-High engagement profiles. Findings have implications for increasing skills-use engagement in daily life to increase literacy performance and suggest differences by demographic characteristics that may be of interest to adult foundational education programs. [This is the online first version of an article published in "Zeitschrift für Weiterbildungsforschung."]

Affine logic is a fragment of continuous logic, introduced by Bagheri, in which only affine functions are allowed as connectives. This has the effect of endowing type spaces with the structure of compact convex sets. We study extremal models of affine theories (those that only realize extreme types), and the ways and conditions under which all models can be described from the extremal ones. We introduce and develop the general theory of measurable fields of metric structures and their direct integrals. One of our main results is an extremal decomposition theorem for models of simplicial theories, that is, affine theories whose type spaces form Choquet simplices. We prove that every model of a simplicial theory can be (uniquely) decomposed as a direct integral of extremal models. This generalizes known decomposition results (ergodic decomposition, tracial von Neumann factor decomposition), and moreover, holds without any separability hypothesis. Two extreme kinds of simplicial theories are Bauer theories, whose extreme types form a closed set, and Poulsen theories, whose extreme types form a dense set. We show that Keisler randomizations of continuous theories are, essentially, the same thing as affine Bauer theories. We establish a dichotomy result: a complete simplicial theory is either Bauer or Poulsen. As part of our analysis, we adapt many results and tools from continuous logic to the affine or extremal contexts (definability, saturation, type isolation, categoricity, etc.). We also provide a detailed study of the relations between continuous logic and affine logic. Finally, we present several examples of simplicial theories arising from theories in discrete logic, Hilbert spaces, probability measure-preserving systems, and tracial von Neumann algebras., Comment: 133 pages

Risk averse decision making under uncertainty in partially observable domains is a fundamental problem in AI and essential for reliable autonomous agents. In our case, the problem is modeled using partially observable Markov decision processes (POMDPs), when the value function is the conditional value at risk (CVaR) of the return. Calculating an optimal solution for POMDPs is computationally intractable in general. In this work we develop a simplification framework to speedup the evaluation of the value function, while providing performance guarantees. We consider as simplification a computationally cheaper belief-MDP transition model, that can correspond, e.g., to cheaper observation or transition models. Our contributions include general bounds for CVaR that allow bounding the CVaR of a random variable X, using a random variable Y, by assuming bounds between their cumulative distributions. We then derive bounds for the CVaR value function in a POMDP setting, and show how to bound the value function using the computationally cheaper belief-MDP transition model and without accessing the computationally expensive model in real-time. Then, we provide theoretical performance guarantees for the estimated bounds. Our results apply for a general simplification of a belief-MDP transition model and support simplification of both the observation and state transition models simultaneously.

High dimensional expanders (HDXs) are a hypergraph generalization of expander graphs. They are extensively studied in the math and TCS communities due to their many applications. Like expander graphs, HDXs are especially interesting for applications when they are bounded degree, namely, if the number of edges adjacent to every vertex is bounded. However, only a handful of constructions are known to have this property, all of which rely on algebraic techniques. In particular, no random or combinatorial construction of bounded degree HDXs is known. As a result, our understanding of these objects is limited. The degree of an $i$-face in an HDX is the number of $(i+1)$-faces containing it. In this work we construct HDXs whose higher dimensional faces have bounded degree. This is done by giving an elementary and deterministic algorithm that takes as input a regular $k$-dimensional HDX $X$ and outputs another $k$-dimensional HDX $\widehat{X}$ with twice as many vertices. While the degree of vertices in $\widehat{X}$ grows, the degree of the $(k-1)$-faces in $\widehat{X}$ stays the same. As a result, we obtain a new `algebra-free' construction of HDXs whose $(k-1)$-face degree is bounded. Our algorithm is based on a simple and natural generalization of the construction by Bilu and Linial (Combinatorica, 2006), which build expanders using lifts coming from edge signings. Our construction is based on local lifts of HDXs, where a local lift is a complex whose top-level links are lifts of links in the original complex. We demonstrate that a local lift of an HDX is an HDX in many cases. In addition, combining local lifts with existing bounded degree constructions creates new families of bounded degree HDXs with significantly different links than before. For every large enough $D$, we use this technique to construct families of bounded degree HDXs with links that have diameter $\geq D$.

One of the benefits of using executable specifications such as Behavioral Programming (BP) is the ability to align the system implementation with its requirements. This is facilitated in BP by a protocol that allows independent implementation modules that specify what the system may, must, and must not do. By that, each module can enforce a single system requirement, including negative specifications such as "don't do X after Y." The existing BP protocol, however, allows only the enforcement of safety requirements and does not support the execution of liveness properties such as "do X at least three times." To model liveness requirements in BP directly and independently, we propose idioms for tagging states with "must-finish," indicating that tasks are yet to be completed. We show that this idiom allows a direct specification of known requirements patterns from the literature. We also offer semantics and two execution mechanisms, one based on a translation to B\"uchi automata and the other based on a Markov decision process (MDP). The latter approach offers the possibility of utilizing deep reinforcement learning (DRL) algorithms, which bear the potential to handle large software systems effectively. This paper presents a qualitative and quantitative assessment of the proposed approach using a proof-of-concept tool. A formal analysis of the MDP-based execution mechanism is given in an appendix., Comment: Accepted to the 32nd IEEE International Requirements Engineering 2024 conference (RE'24)

We consider a stock that follows a geometric Brownian motion (GBM) and a riskless asset continuously compounded at a constant rate. We assume that the stock can go bankrupt, i.e., lose all of its value, at some exogenous random time (independent of the stock price) modeled as the first arrival time of a homogeneous Poisson process. For this setup, we study Merton's optimal portfolio problem consisting in maximizing the expected isoelastic utility of the total wealth at a given finite maturity time. We obtain an analytical solution using coupled Hamilton-Jacobi-Bellman (HJB) equations. The optimal strategy bans borrowing and never allocates more wealth into the stock than the classical Merton ratio recommends. For non-logarithmic isoelastic utilities, the optimal weights are non-myopic. This is an example where a realistic problem, being merely a slight modification of the usual GBM model, leads to non-myopic weights. For logarithmic utility, we additionally present an alternative derivation using a stochastic integral and verify that the weights obtained are identical to our first approach. We also present an example for our strategy applied to a stock with non-zero bankruptcy probability., Comment: 16 pages, 2 figure

We establish a separation principle for the output feedback stabilisation of state-affine systems that are observable at the stabilization target. Relying on control templates (recently introduced in [4]), that allow to approximate a feedback control while maintaining observability, we design a closed loop hybrid state-observer system that we show to be semi-globally asymptotically stable. Under assumption of polynomiality of the system with respect to the control, we give an explicit construction of control templates. We illustrate the results of the paper with numerical simulations.

We derive presentation and relations for a group of compact Riemann surface that is given as branched cover of the sphere. In the case that one of the permutations is of full cycle of the form $(1...n)$ we derive a straightforward process to obtain the standard presentation of the fundamental group of Algebraic curve in the form $\prod_{i=1}^g[a_i,b_i]=1$

In this paper we formulate and solve an optimal problem for Stochastic process with a regime absorbing state. The solution for this problem is obtained through a system of partial differential equations. The method is applied to obtain an explicit solution for the Merton portfolio problem when an asset has a default probability in case of a log utility., Comment: 7 pages

We express the branch points cross ratio of Hyper-elliptic Mumford curves as quotients of p adic theta functions evaluated at the p adic period matrix, Comment: 7 pages, no figures. preliminary draft

These notes form part of a joint research project on the logic of fields with many valuations, connected by a product formula. We define such structures and name them {\em globally valued fields} (GVFs). This text aims primarily at a proof that {\em the canonical GVF structure on $k(t)^{alg}$ is existentially closed}. This can be read as saying that a variety {\em with a distinguished curve class} is a good approximation for a formula in the language of GVFs, in the same way that a variety is close to a formula for the theory ACF of algebraically closed fields.

Purpose: This study explores the roles of morphological skills (Morphological Awareness, Morphological-Syntactic-Knowledge, Morphological-Semantic-Knowledge, and Morphological-Orthographic/Phonological-Knowledge), vocabulary (knowledge of definitions, relationships between words, and polysemous meanings), and syntax in contributing to adolescent reading comprehension. Specifically, we identify the relative importance of these language skills. Methods: A racially diverse sample of 1,027 students grades 5 to 8 were studied. Dominance Analysis was used, which allows a rank ordering of the contribution of predictors. Results: Results suggest unique roles for each language area with particularly important roles for vocabulary and morphological awareness. Considering just morphology, four morphology skills each explained meaningful variance (13-17%) in reading comprehension, together explaining half the variance in standardized reading comprehension. Considering each language area, vocabulary, the four morphology skills, and syntax were shown to each explain meaningful variance, ranging from 9-13%, together explaining 62.9% of the variance in reading comprehension. Conclusions: Findings are interpreted within the Reading Systems framework. Findings confirm the role of vocabulary, morphology, and syntax in supporting reading comprehension and suggest a relatively stronger role for vocabulary and morphological awareness. The meaningful role of the four morphological skills also suggests a broad role for morphology. Implications for theory, research, and practice are shared. [This paper will be published in "Scientific Studies of Reading."]

Given a continuous and isometric action of a Polish group $G$ on an adequate Polish topometric space $(X,\tau,\rho)$ and $x \in X$, we find a necessary and sufficient condition for $\overline{Gx}^\rho$ to be co-meagre; we also obtain a criterion that characterizes when such a point exists. This work completes a criterion established in earlier work of the authors.