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We consider a stochastic volatility model where the price evolution depend on the exponential of the Ornstein--Uhlenbeck process. After a brief revision of the related theory the entropy-minimal equivalent martingale measure. is calculated., Comment: 9 pages, 2 figures

The interface between a ferromagnetic metal and an organic molecular semiconductor, commonly referred to as a spinterface, is an important component for advancing spintronic technologies. Hybridization of the ferromagnetic-metal surface d orbitals with the molecular-semiconductor p orbitals induces profound modifications not only in the interfacial molecular layer, but also in the surface ferromagnetic-metal atomic layer. These effects are particularly pronounced at low temperatures, manifesting as substantial modifications in the magnetic properties of thin-film magnetic-metal/organic heterostructures. Despite extensive research and interest, the magnetic-ordering and magnetic-properties of the spinterface remain poorly understood. Using ultrafast time-resolved magneto-optical spectroscopy, to investigate the magnetic dynamics in such heterostructures, we unveil the unique spinterface-magnetism and its universality for a broad variety of cobalt/molecular-semiconductor interfaces. In particular, our findings demonstrate the presence of highly anisotropic low-temperature superparamagnetism at the cobalt/molecular-semiconductor spinterface. This anisotropic interfacial superparamagnetism is likely driven by strong chemical modifications in the cobalt interfacial layer caused by the chemisorbed molecular layer. These results highlight the pivotal role of molecular chemisorption in tuning the magnetic properties at spinterfaces, paving the way for future spintronic applications.

We develop a quantum Boltzman equation approach that incorporates microscopic impurity models into the theory of orbital transport, revealing, how impurity properties, including their symmetry, influence the relaxation of orbital momentum and the orbital Hall effect. Specifically, we demonstrate that when the impurity potential has axial symmetry, the relaxation is governed by the Dyakonov-Perel mechanism. In contrast, when this symmetry is broken, scattering can result in a rapid Elliot-Yafet relaxation of orbital momentum. The details of impurity potential also affect the intrinsic orbital Hall effect even when the impurity concentration is very small. Impurities that alter the orbital texture can also give rise to a skew-scattering contribution to the orbital Hall effect, although this does not necessarily dominate in materials that are nearly pristine due to the Dyakonov-Perel relaxation., Comment: 15 pages, 6 figures

The study deals with the ruin problem when an insurance company invests its reserve in a risky asset whose the price dynamics is given by a geometric L\'evy process. Considering the ruin probability as a of the capital reserve we obtain for it a partial integro-differential equation understood in a viscosity sense and prove a result on the uniqueness of the viscosity solution for a corresponding boundary value problem., Comment: 13 pages

We expose a simple solution of the consumption-investment problem pair trading. The proof is based on the remark that the HJB equation can be reduced to a linear parabolic equation solvable explicitly.

The paper deals with the ruin problem of an insurance company investing its capital reserve in a risky asset with the price dynamics given by a conditional geometric Brownian motion whose parameters depend on a Markov process describing a random variations in the economic and financial environments. We prove smoothness of the ruin probability as a function of the initial capital and obtain for it an integro-differential equation.

In the cuprates, the opening of a d-wave superconducting (SC) gap is accompanied by a redistribution of spectral weight at energies two orders of magnitude larger than this gap. This indicates the importance to the pairing mechanism of on-site electronic excitations, such as orbital transitions or charge transfer excitations. Here, we resort to a three-pulse pump-probe scheme to study the broadband non-equilibrium dielectric function in optimally-doped $Bi_2Sr_2Ca_{0.92}Y_{0.08}Cu_2O_{8+{\delta}}$ and we identify two distinct dynamical responses: i) a blueshift of the central energy of an interband excitation peaked at 2 eV and ii) a change in spectral weight in the same energy range. Photoexcitation with near-IR and mid-IR pulses, with photon energies respectively above and below the SC gap, reveals that the transient changes in the central energy are not modified by the onset of superconductivity and do not depend on the pump photon energy. Conversely, the spectral weight dynamics strongly depends on the pump photon energy and has a discontinuity at the critical temperature. The picture that emerges is that, while high-energy pulses excite quasiparticles in both nodal and thermally inaccessible antinodal states, photoexcitation by low-energy pulses mostly accelerates the condensate and creates excitations predominantly at the nodes of the SC gap. These results, rationalized by kinetic equations for d-wave superconducting gaps, indicate that dynamical control of the momentum-dependent distribution of non-thermal quasiparticles may be achieved by the selective tuning of the photoexcitation.

The spin phenomena observed at a clean metall-insulator interface are typically reduced to Rashba-Edelstein effect, that leads to spin accumulation over a few monolayers. We demonstrate that the presence of interface disorder significantly expands the range of potential phenomena. Specifically, the skew scattering at the metal - insulator boundary gives rise to the "kinetic Rashba-Edelstein effect", where spin accumulation occurs on a much larger length scale comparable to mean free path. Moreover, at higher orders of spin-orbit interaction, skew scattering is accompanied with spin relaxation resulting in the interface spin-Hall effect - a conversion of electrical current to spin current at the metal surface. Unlike the conventional spin-Hall effect, this phenomenon persists even within the Born approximation. These two predicted phenomena can dominate the spin density and spin current in devices of intermediate thickness., Comment: Accepted in Phys. Rev. Research

We study THz-driven condensate dynamics in epitaxial thin films of MgB$_{2}$, a prototype two-band superconductor (SC) with weak interband coupling. The temperature and excitation density dependent dynamics follow the behavior predicted by the phenomenological bottleneck model for the single-gap SC, implying adiabatic coupling between the two condensates on the ps timescale. The amplitude of the THz-driven suppression of condensate density reveals an unexpected decrease in pair-breaking efficiency with increasing temperature - unlike in the case of optical excitation. The reduced pair-breaking efficiency of narrow-band THz pulses, displaying minimum near $\approx0.7$ T$_{c}$, is attributed to THz-driven, long-lived, non-thermal quasiparticle distribution, resulting in Eliashberg-type enhancement of superconductivity, competing with pair-breaking.

In 2022, the second author found a prolific construction of strongly regular graphs, which is based on joining a coclique and a divisible design graph with certain parameters. The construction produces strongly regular graphs with the same parameters as the complement of the symplectic graph $\mathsf{Sp}(2d,q)$. In this paper, we determine the parameters of strongly regular graphs which admit a decomposition into a divisible design graph and a coclique attaining the Hoffman bound. In particular, it is shown that when the least eigenvalue of such a strongly regular graph is a prime power, its parameters coincide with those of the complement of $\mathsf{Sp}(2d,q)$. Furthermore, a generalization of the construction is discussed.

This note is a complement to the paper by Eberlein, Kabanov, and Schmidt on the asymptotic of the ruin probability in a Sparre Andersen non-life insurance model with investments a risky asset whose price follows a geometric L\'evy process. Using the techniques of semi-Markov processes we extend the result of the mentioned paper to the case of annuities and models with two-sided jumps.

We study a model of clearing in an interbank network with crossholdings and default charges. Following the Eisenberg--Noe approach, we define the model via a set of natural financial regulations including those related with eventual default charges and derive a finite family of fixpoint problems. These problems are parameterized by vectors of binary variables. Our model combines features of the Ararat--Meimanjanov, Rogers--Veraart, and Suzuki--Elsinger networks. We develop methods of computing the maximal and minimal clearing pairs using the mixed integer-linear programming and a Gaussian elimination algorithm., Comment: 10 pages

The paper discusses the improvement of the accuracy of an inertial navigation system created on the basis of MEMS sensors using machine learning (ML) methods. As input data for the classifier, we used infor-mation obtained from a developed laboratory setup with MEMS sensors on a sealed platform with the ability to adjust its tilt angles. To assess the effectiveness of the models, test curves were constructed with different values of the parameters of these models for each core in the case of a linear, polynomial radial basis function. The inverse regularization parameter was used as a parameter. The proposed algorithm based on MO has demonstrated its ability to correctly classify in the presence of noise typical for MEMS sensors, where good classification results were obtained when choosing the optimal values of hyperpa-rameters., Comment: 7 pages, 5 figures, 5 formulas

High-power femtosecond laser radiation propagates nonlinearly in air exhibiting pulse self-focusing and strong multiphoton medium ionization, which leads to the spatial fragmentation of laser pulse into highly-localized light channels usually called the filaments. The filaments are characterized by high optical intensity, reduced (even zero) angular spreading and can contain laser plasma or be plasmaless (postfilaments). The presence of optical turbulence on the propagation path dramatically changes pulse filamentation dynamics and in some cases causes pulse fragmentation enhancement and collapse arrest. For the first time to our knowledge, we experimentally and theoretically investigate the transverse profile of Ti:sapphire femtosecond laser radiation nonlinearly propagating a 65 m air path to the region of postfilament evolution after passing through an artificial localized air turbulence. We show that when a turbulent layer is placed before the filamentation region, the average number of high-intensive local fluence maxima ("hot points") in pulse profile as well as their sizes grow as the turbulence strength increases, and then saturates at some levels. On the contrary, the deposition of a turbulent screen within the filamentation region has almost no effect on both the number and the average diameter of the postfilaments.

Cryo-computing is presently severely limited by the absence of a suitable fast and energy efficient cryo-memory. Ideally, such memory should be compatible with single-flux quantum (SFQ) logic in terms of speed, switching energy and matching impedance. Here we present an implementation of non-volatile charge configuration memory (CCM) in a cryo-computing environment by combining it in parallel with a pulse-triggered superconducting nanowire cryotron (nTron). The combined device is modeled in terms of the dynamical response of the SC order parameter in a current-controlled nanowire with a CCM shunt. Analysis of timedynamics and current-voltage characteristics based on measured device parameters show that single flux quantum (SFQ)-level pulses can drive non-volatile CCM on the picosecond timescale, while allowing the nTron to operate in non-latching mode. The inherent high energy efficiency and ultrahigh speed makes this hybrid device an ideal memory for use in cryo-computing and quantum computing peripheral devices.

The symplectic graph Sp(2d, q) is the collinearity graph of the symplectic space of dimension 2d over a finite field of order q. A k-regular graph on v vertices is a divisible design graph with parameters (v, k, lambda_1, lambda_2 ,m,n) if its vertex set can be partitioned into m classes of size n, such that any two different vertices from the same class have lambda_1 common neighbours, and any two vertices from different classes have lambda_2 common neighbours whenever it is not complete or edgeless. In this paper we propose a new construction of strongly regular graphs with the parameters of the complement of the symplectic graph using divisible design graphs., Comment: 9 pages

Noisy intermediate-scale quantum (NISQ) devices are spearheading the second quantum revolution. Of these, quantum annealers are the only ones currently offering real world, commercial applications on as many as 5000 qubits. The size of problems that can be solved by quantum annealers is limited mainly by errors caused by environmental noise and intrinsic imperfections of the processor. We address the issue of intrinsic imperfections with a novel error correction approach, based on machine learning methods. Our approach adjusts the input Hamiltonian to maximize the probability of finding the solution. In our experiments, the proposed error correction method improved the performance of annealing by up to three orders of magnitude and enabled the solving of a previously intractable, maximally complex problem.

A k-regular graph on v vertices is a divisible design graph with parameters (v, k, lambda_1 ,lambda_2, m, n) if its vertex set can be partitioned into m classes of size n, such that any two different vertices from the same class have lambda_1 common neighbours, and any two vertices from different classes have lambda_2 common neighbours whenever it is not complete or edgeless. If m=1, then a divisible design graph is strongly regular with parameters (v, k, lambda_1, lambda_1). In this paper the Wallis-Fon-Der-Flaass construction of strongly regular graphs is modified to create new constructions of divisible design graphs. In some cases, these constructions lead to strongly regular graphs., Comment: 13 pages