arXiv subjects

Asaf Cohen

Publications and source records attributed to Asaf Cohen.

At least 37 records · Page 2Linked to original sources

arXiv2025

On the light-curves of disk and bulge novae

We examine the light curves of a sample of novae, classifying them into single-peaked and multiple-peaked morphologies. Using accurate distances from Gaia, we determine the spatial distribution of these novae by computing their heights, $Z$, above the Galactic plane. We show that novae exhibiting a single peak in their light curves tend to concentrate near the Galactic plane, while those displaying multiple peaks are more homogeneously distributed, reaching heights up to 1000 pc above the plane. A KS test rejects the null hypothesis that the two distributions originate from the same population at a significance level corresponding to $4.2σ$.

astro-ph.GA↗

arXiv2025

Covert Adversarial Actuators in Finite MDPs

We consider a Markov decision process (MDP) in which actions prescribed by the controller are executed by a separate actuator, which may behave adversarially. At each time step, the controller selects and transmits an action to the actuator; however, the actuator may deviate from the intended action to degrade the control reward. Given that the controller observes only the sequence of visited states, we investigate whether the actuator can covertly deviate from the controller's policy to minimize its reward without being detected. We establish conditions for covert adversarial behavior over an infinite time horizon and formulate an optimization problem to determine the optimal adversarial policy under these conditions. Additionally, we derive the asymptotic error exponents for detection in two scenarios: (1) a binary hypothesis testing framework, where the actuator either follows the prescribed policy or a known adversarial strategy, and (2) a composite hypothesis testing framework, where the actuator may employ any stationary policy. For the latter case, we also propose an optimization problem to maximize the adversary's performance.

cs.IT↗

arXiv2025

PIR Over Wireless Channels: Achieving Privacy With Public Responses

In this paper, we address the problem of Private Information Retrieval (PIR) over a public Additive White Gaussian Noise (AWGN) channel. In such a setup, the server's responses are visible to other servers. Thus, a curious server can listen to the other responses, compromising the user's privacy. Indeed, previous works on PIR over a shared medium assumed the servers cannot instantaneously listen to other responses. To address this gap, we present a novel randomized lattice -- PIR coding scheme that jointly codes for privacy, channel noise, and curious servers which may listen to other responses. We demonstrate that a positive PIR rate is achievable even in cases where the channel to the curious server is stronger than the channel to the user.

cs.IT↗

arXiv2024

Deep Backward and Galerkin Methods for the Finite State Master Equation

This paper proposes and analyzes two neural network methods to solve the master equation for finite-state mean field games (MFGs). Solving MFGs provides approximate Nash equilibria for stochastic, differential games with finite but large populations of agents. The master equation is a partial differential equation (PDE) whose solution characterizes MFG equilibria for any possible initial distribution. The first method we propose relies on backward induction in a time component while the second method directly tackles the PDE without discretizing time. For both approaches, we prove two types of results: there exist neural networks that make the algorithms' loss functions arbitrarily small, and conversely, if the losses are small, then the neural networks are good approximations of the master equation's solution. We conclude the paper with numerical experiments on benchmark problems from the literature up to dimension 15, and a comparison with solutions computed by a classical method for fixed initial distributions.

math.OC↗

arXiv2024

Correction to "Private Information Retrieval Over Gaussian MAC"

In the above article \cite{shmuel2021private}, the authors introduced a PIR scheme for the Additive White Gaussian Noise (AWGN) Multiple Access Channel (MAC), both with and without fading. The authors utilized the additive nature of the channel and leveraged the linear properties and structure of lattice codes to retrieve the desired message without the servers acquiring any knowledge about the retrieved message's index. Theorems 3 and 4 in \cite{shmuel2021private} contain an error arising from the incorrect usage of the modulo operator. Moreover, the proofs assume a one-to-one mapping function, $ϕ(\cdot)$, between a message $W_j\in\mathbb{F}_p^L$ and the elements of $\cC$, mistakenly suggesting that the user possesses all the required information in advance. % \st{However, this is not the case.} \textcolor{black}{To deal with that, we defined $ϕ(\cdot)$ as a one-to-one mapping function between a vector of $l$ information bits and a lattice point $λ\in\cC$}. Herein, we present the corrected versions of these theorems.

cs.IT↗

arXiv2024

DEX Specs: A Mean Field Approach to DeFi Currency Exchanges

We investigate the behavior of liquidity providers (LPs) by modeling a decentralized cryptocurrency exchange (DEX) based on Uniswap v3. LPs with heterogeneous characteristics choose optimal liquidity positions subject to uncertainty regarding the size of exogenous incoming transactions and the prices of assets in the wider market. They engage in a game among themselves, and the resulting liquidity distribution determines the exchange rate dynamics and potential arbitrage opportunities of the pool. We calibrate the distribution of LP characteristics based on Uniswap data and the equilibrium strategy resulting from this mean-field game produces pool exchange rate dynamics and liquidity evolution consistent with observed pool behavior. We subsequently introduce Maximal Extractable Value (MEV) bots who perform Just-In-Time (JIT) liquidity attacks, and develop a Stackelberg game between LPs and bots. This addition results in more accurate simulated pool exchange rate dynamics and stronger predictive power regarding the evolution of the pool liquidity distribution.

q-fin.TR↗

arXiv2023

Learning-based Optimal Admission Control in a Single Server Queuing System

We consider a long-term average profit maximizing admission control problem in an M/M/1 queuing system with unknown service and arrival rates. With a fixed reward collected upon service completion and a cost per unit of time enforced on customers waiting in the queue, a dispatcher decides upon arrivals whether to admit the arriving customer or not based on the full history of observations of the queue-length of the system. (Naor 1969, Econometrica) showed that if all the parameters of the model are known, then it is optimal to use a static threshold policy -- admit if the queue-length is less than a predetermined threshold and otherwise not. We propose a learning-based dispatching algorithm and characterize its regret with respect to optimal dispatch policies for the full information model of Naor (1969). We show that the algorithm achieves an $O(1)$ regret when all optimal thresholds with full information are non-zero, and achieves an $O(\ln^{1+ε}(N))$ regret for any specified $ε>0$, in the case that an optimal threshold with full information is $0$ (i.e., an optimal policy is to reject all arrivals), where $N$ is the number of arrivals.

math.OC↗

arXiv2023

Quantum-inspired nonlinear Galerkin ansatz for high-dimensional HJB equations

Neural networks are increasingly recognized as a powerful numerical solution technique for partial differential equations (PDEs) arising in diverse scientific computing domains, including quantum many-body physics. In the context of time-dependent PDEs, the dominant paradigm involves casting the approximate solution in terms of stochastic minimization of an objective function given by the norm of the PDE residual, viewed as a function of the neural network parameters. Recently, advancements have been made in the direction of an alternative approach which shares aspects of nonlinearly parametrized Galerkin methods and variational quantum Monte Carlo, especially for high-dimensional, time-dependent PDEs that extend beyond the usual scope of quantum physics. This paper is inspired by the potential of solving Hamilton-Jacobi-Bellman (HJB) PDEs using Neural Galerkin methods and commences the exploration of nonlinearly parametrized trial functions for which the evolution equations are analytically tractable. As a precursor to the Neural Galerkin scheme, we present trial functions with evolution equations that admit closed-form solutions, focusing on time-dependent HJB equations relevant to finance.

math.NA↗

arXiv2023

A neural network approach to high-dimensional optimal switching problems with jumps in energy markets

We develop a backward-in-time machine learning algorithm that uses a sequence of neural networks to solve optimal switching problems in energy production, where electricity and fossil fuel prices are subject to stochastic jumps. We then apply this algorithm to a variety of energy scheduling problems, including novel high-dimensional energy production problems. Our experimental results demonstrate that the algorithm performs with accuracy and experiences linear to sub-linear slowdowns as dimension increases, demonstrating the value of the algorithm for solving high-dimensional switching problems.

math.OC↗

arXiv2023

Order-optimal Joint Transmission and Identification in Massive Multi-User MIMO via Group Testing

The number of wireless devices which are connected to a single Wireless Local Area Network continues to grow each year. As a result, the orchestration of so many devices becomes a daunting, resource--consuming task, especially when the resources available at the single access point are limited, and it is hard to anticipate which devices will request access at any given time. On the other hand, the number of antennas on both the devices and the access point grows as well, facilitating advanced joint scheduling and coding techniques. In this paper, we leverage the large number of antennas and suggest a massive multiple-user multiple-input-multiple-output (MU-MIMO) scheme using sparse coding based on Group Testing (GT) principles. The scheme allows for a small subset of devices to transmit simultaneously, without a preceding scheduling phase or coordination, thus reducing overhead and complexity. Specifically, we show that out of a population of $N$ devices, it is possible to jointly identify and decode $K$ devices, unknown in advance, simultaneously and without any scheduling. The scheme utilizes minimal knowledge of channel state, uses an efficient (in both run-time and space) decoding algorithm, and requires $O(K\log N\mathcal{M})$ antennas, where $\mathcal{M}$ is the number of messages per device. In fact, we prove that this scheme is order--optimal in the number of users and messages. This is done by deriving sufficient conditions for a vanishing error probability (a direct result), bounding the minimal number of antennas necessary for any such scheme (a converse result), and showing that these results are asymptotically tight.

cs.IT↗

arXiv2022

Covertly Controlling a Linear System

Consider the problem of covertly controlling a linear system. In this problem, Alice desires to control (stabilize or change the behavior of) a linear system, while keeping an observer, Willie, unable to decide if the system is indeed being controlled or not. We formally define the problem, under a model where Willie can only observe the system's output. Focusing on AR(1) systems, we show that when Willie observes the system's output through a clean channel, an inherently unstable linear system can not be covertly stabilized. However, an inherently stable linear system can be covertly controlled, in the sense of covertly changing its parameter or resetting its memory. Moreover, we give positive and negative results for two important controllers: a minimal-information controller, where Alice is allowed to use only $1$ bit per sample, and a maximal-information controller, where Alice is allowed to view the real-valued output. Unlike covert communication, where the trade-off is between rate and covertness, the results reveal an interesting \emph{three--fold} trade--off in covert control: the amount of information used by the controller, control performance and covertness.

cs.IT↗

arXiv2022

Analysis of the Finite-State Ergodic Master Equation

Mean field games model equilibria in games with a continuum of players as limiting systems of symmetric $n$-player games with weak interaction between the players. We consider a finite-state, infinite-horizon problem with two cost criteria: discounted and ergodic. Under the Lasry--Lions monotonicity condition we characterize the stationary ergodic mean field game equilibrium by a mean field game system of two coupled equations: one for the value and the other for the stationary measure. This system is linked with the ergodic master equation. Several discounted mean field game systems are utilized in order to set up the relevant discounted master equations. We show that the discounted master equations are smooth, uniformly in the discount factor. Taking the discount factor to zero, we achieve the smoothness of the ergodic master equation.

math.AP↗

arXiv2022

Quantum-inspired variational algorithms for partial differential equations: Application to financial derivative pricing

Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real- and imaginary time-dependent Schrödinger equation. In this paper, we present a simple generalization of VMC applicable to arbitrary time-dependent PDEs, showcasing the technique in the multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets.

math.NA↗

arXiv2022

A Scaling Limit for Utility Indifference Prices in the Discretized Bachelier Model

We consider the discretized Bachelier model where hedging is done on an equidistant set of times. Exponential utility indifference prices are studied for path-dependent European options and we compute their non-trivial scaling limit for a large number of trading times $n$ and when risk aversion is scaled like $n\ell$ for some constant $\ell>0$. Our analysis is purely probabilistic. We first use a duality argument to transform the problem into an optimal drift control problem with a penalty term. We further use martingale techniques and strong invariance principles and get that the limiting problem takes the form of a volatility control problem.

math.PR↗

arXiv2022

Covertly Controlling a Linear System

Consider the problem of covertly controlling a linear system. In this problem, Alice desires to control (stabilize or change the parameters of) a linear system, while keeping an observer, Willie, unable to decide if the system is indeed being controlled or not. We formally define the problem, under two different models: (i) When Willie can only observe the system's output (ii) When Willie can directly observe the control signal. Focusing on AR(1) systems, we show that when Willie observes the system's output through a clean channel, an inherently unstable linear system can not be covertly stabilized. However, an inherently stable linear system can be covertly controlled, in the sense of covertly changing its parameter. Moreover, we give direct and converse results for two important controllers: a minimal-information controller, where Alice is allowed to used only $1$ bit per sample, and a maximal-information controller, where Alice is allowed to view the real-valued output. Unlike covert communication, where the trade-off is between rate and covertness, the results reveal an interesting \emph{three--fold} trade--off in covert control: the amount of information used by the controller, control performance and covertness. To the best of our knowledge, this is the first study formally defining covert control.

math.OC↗

arXiv2021

Universal Randomized Guessing Subjected to Distortion

In this paper, we consider the problem of guessing a sequence subject to a distortion constraint. Specifically, we assume the following game between Alice and Bob: Alice has a sequence $\bx$ of length $n$. Bob wishes to guess $\bx$, yet he is satisfied with finding any sequence $\hat{\bx}$ which is within a given distortion $D$ from $\bx$. Thus, he successively submits queries to Alice, until receiving an affirmative answer, stating that his guess was within the required distortion. Finding guessing strategies which minimize the number of guesses (the \emph{guesswork}), and analyzing its properties (e.g., its $ρ$--th moment) has several applications in information security, source and channel coding. Guessing subject to a distortion constraint is especially useful when considering contemporary biometrically--secured systems, where the "password" which protects the data is not a single, fixed vector but rather a \emph{ball of feature vectors} centered at some $\bx$, and any feature vector within the ball results in acceptance. We formally define the guessing problem under distortion in \emph{four different setups}: memoryless sources, guessing through a noisy channel, sources with memory and individual sequences. We suggest a randomized guessing strategy which is asymptotically optimal for all setups and is \emph{five--fold universal}, as it is independent of the source statistics, the channel, the moment to be optimized, the distortion measure and the distortion level.

cs.IT↗

arXiv2021

Finite state mean field games with Wright Fisher common noise as limits of $N$-player weighted games

Forcing finite state mean field games by a relevant form of common noise is a subtle issue, which has been addressed only recently. Among others, one possible way is to subject the simplex valued dynamics of an equilibrium by a so-called Wright-Fisher noise, very much in the spirit of stochastic models in population genetics. A key feature is that such a random forcing preserves the structure of the simplex, which is nothing but, in this setting, the probability space over the state space of the game. The purpose of this article is hence to elucidate the finite player version and, accordingly, to prove that $N$-player equilibria indeed converge towards the solution of such a kind of Wright-Fisher mean field game. Whilst part of the analysis is made easier by the fact that the corresponding master equation has already been proved to be uniquely solvable under the presence of the common noise, it becomes however more subtle than in the standard setting because the mean field interaction between the players now occurs through a weighted empirical measure. In other words, each player carries its own weight, which hence may differ from $1/N$ and which, most of all, evolves with the common noise.

math.PR↗

arXiv2021

Optimal Dividends under Model Uncertainty

We consider a diffusive model for optimally distributing dividends, while allowing for Knightian model ambiguity concerning the drift of the surplus process. We show that the value function is the unique solution of a non-linear Hamilton-Jacobi-Bellman variational inequality. In addition, this value function embodies a unique optimal threshold strategy for the insurer's surplus, thereby making it the smooth pasting of a non-linear and linear part at the location of the threshold. Furthermore, we obtain continuity and monotonicity of the value function and the threshold strategy with respect to the parameter that measures ambiguity of our model.

math.OC↗