We formulate option market making as a constrained, risk-sensitive control problem that unifies execution, hedging, and arbitrage-free implied-volatility surfaces inside a single learning loop. A fully differentiable eSSVI layer enforces static no-arbitrage conditions (butterfly and calendar) while the policy controls half-spreads, hedge intensity, and structured surface deformations (state-dependent rho-shift and psi-scale). Executions are intensity-driven and respond monotonically to spreads and relative mispricing; tail risk is shaped with a differentiable CVaR objective via the Rockafellar--Uryasev program. We provide theory for (i) grid-consistency and rates for butterfly/calendar surrogates, (ii) a primal--dual grounding of a learnable dual action acting as a state-dependent Lagrange multiplier, (iii) differentiable CVaR estimators with mixed pathwise and likelihood-ratio gradients and epi-convergence to the nonsmooth objective, (iv) an eSSVI wing-growth bound aligned with Lee's moment constraints, and (v) policy-gradient validity under smooth surrogates. In simulation (Heston fallback; ABIDES-ready), the agent attains positive adjusted P\&L on most intraday segments while keeping calendar violations at numerical zero and butterfly violations at the numerical floor; ex-post tails remain realistic and can be tuned through the CVaR weight. The five control heads admit clear economic semantics and analytic sensitivities, yielding a white-box learner that unifies pricing consistency and execution control in a reproducible pipeline.

This study investigated the dynamic connectivity patterns between EEG and fMRI modalities, contributing to our understanding of brain network interactions. By employing a comprehensive approach that integrated static and dynamic analyses of EEG-fMRI data, we were able to uncover distinct connectivity states and characterize their temporal fluctuations. The results revealed modular organization within the intrinsic connectivity networks (ICNs) of the brain, highlighting the significant roles of sensory systems and the default mode network. The use of a sliding window technique allowed us to assess how functional connectivity varies over time, further elucidating the transient nature of brain connectivity. Additionally, our findings align with previous literature, reinforcing the notion that cognitive states can be effectively identified through short-duration data, specifically within the 30-60 second timeframe. The established relationships between connectivity strength and cognitive processes, particularly during different visual states, underscore the relevance of our approach for future research into brain dynamics. Overall, this study not only enhances our understanding of the interplay between EEG and fMRI signals but also paves the way for further exploration into the neural correlates of cognitive functions and their implications in clinical settings. Future research should focus on refining these methodologies and exploring their applications in various cognitive and clinical contexts.

We present a new explanation for a quantum eraser. Mathematical description of the traditional explanation needs quantum-superposition states. However, the phenomenon can be explained without quantum-superposition states by introducing unobservable potentials which can be identified as an indefinite metric vector. In addition, a delayed choice experiment can also be explained by the interference between the photons and unobservable potentials, which seems like an unreal long-range correlation beyond the causality.

The analysis of the USA 2001 income distribution shows that it can be described by at least two main components, which obey the generalized Tsallis statistics with different values of the q parameter. Theoretical calculations using the gas kinetics model with a distributed saving propensity factor and two ensembles reproduce the empirical data and provide further information on the structure of the distribution, which shows a clear stratification. This stratification is amenable to different interpretations, which are analyzed. The distribution function is invariant with the average individual income, which implies that the inequity of the distribution cannot be modified by increasing the total income.

We study the primary DNA structure of four of the most completely sequenced human chromosomes (including chromosome 19 which is the most dense in coding), using Non-extensive Statistics. We show that the exponents governing the decay of the coding size distributions vary between $5.2 \le r \le 5.7$ for the short scales and $1.45 \le q \le 1.50$ for the large scales. On the contrary, the exponents governing the decay of the non-coding size distributions in these four chromosomes, take the values $2.4 \le r \le 3.2$ for the short scales and $1.50 \le q \le 1.72$ for the large scales. This quantitative difference, in particular in the tail exponent $q$, indicates that the non-coding (coding) size distributions have long (short) range correlations. This non-trivial difference in the DNA statistics is attributed to the non-conservative (conservative) evolution dynamics acting on the non-coding (coding) DNA sequences.

We analyze gene expression time-series data of yeast S. cerevisiae measured along two full cell-cycles. We quantify these data by using q-exponentials, gene expression ranking and a temporal mean-variance analysis. We construct gene interaction networks based on correlation coefficients and study the formation of the corresponding giant components and minimum spanning trees. By coloring genes according to their cell function we find functional clusters in the correlation networks and functional branches in the associated trees. Our results suggest that a percolation point of functional clusters can be identified on these gene expression correlation networks.

De novo genome assembly is a relevant but computationally complex task in genomics. Although de novo assemblers have been used successfully in several genomics projects, there is still no 'best assembler', and the choice and setup of assemblers still rely on bioinformatics experts. Thus, as with other computationally complex problems, machine learning may emerge as an alternative (or complementary) way for developing more accurate and automated assemblers. Reinforcement learning has proven promising for solving complex activities without supervision - such games - and there is a pressing need to understand the limits of this approach to 'real' problems, such as the DFA problem. This study aimed to shed light on the application of machine learning, using reinforcement learning (RL), in genome assembly. We expanded upon the sole previous approach found in the literature to solve this problem by carefully exploring the learning aspects of the proposed intelligent agent, which uses the Q-learning algorithm, and we provided insights for the next steps of automated genome assembly development. We improved the reward system and optimized the exploration of the state space based on pruning and in collaboration with evolutionary computing. We tested the new approaches on 23 new larger environments, which are all available on the internet. Our results suggest consistent performance progress; however, we also found limitations, especially concerning the high dimensionality of state and action spaces. Finally, we discuss paths for achieving efficient and automated genome assembly in real scenarios considering successful RL applications - including deep reinforcement learning.

Tsallis' non-extensive entropy is extended to incorporate the dependence on affinities between the microstates of a system. At the core of our construction of the extended entropy ($\mathcal{H}$) is the concept of the effective number of dissimilar states, termed the effective diversity ($\mathitΔ$). It is a unique integrated measure derived from the probability distribution among states and the affinities between states. The effective diversity is related to the extended entropy through the Boltzmann's-equation-like relation, $\mathcal{H}=\ln_{q}\mathitΔ$, in terms of the Tsallis' $q$-logarithm. A new principle called the Nesting Principle is established, stating that the effective diversity remains invariant under an arbitrary grouping of the constituent states. It is shown that this invariance property holds only for $q=2$; however, the invariance is recovered for general $q$ in the zero-affinity limit (i.e. the Tsallis and Boltzmann-Gibbs case). Using the affinity-based extended Tsallis entropy, the microcanonical and the canonical ensembles are constructed in the presence of general between-state affinities. It is shown that the classic postulate of equal a priori probabilities no longer holds but is modified by affinity-dependent terms. As an illustration, a two-level system is investigated by the extended canonical method, which manifests that the thermal behaviours of the thermodynamic quantities at equilibrium are affected by the between-state affinity. Furthermore, some applications and implications of the affinity-based extended diversity/entropy for information theory and biodiversity theory are addressed in appendices.

Artificial Intelligence (AI) has become commonplace to solve routine everyday tasks. Because of the exponential growth in medical imaging data volume and complexity, the workload on radiologists is steadily increasing. We project that the gap between the number of imaging exams and the number of expert radiologist readers required to cover this increase will continue to expand, consequently introducing a demand for AI-based tools that improve the efficiency with which radiologists can comfortably interpret these exams. AI has been shown to improve efficiency in medical-image generation, processing, and interpretation, and a variety of such AI models have been developed across research labs worldwide. However, very few of these, if any, find their way into routine clinical use, a discrepancy that reflects the divide between AI research and successful AI translation. To address the barrier to clinical deployment, we have formed MONAI Consortium, an open-source community which is building standards for AI deployment in healthcare institutions, and developing tools and infrastructure to facilitate their implementation. This report represents several years of weekly discussions and hands-on problem solving experience by groups of industry experts and clinicians in the MONAI Consortium. We identify barriers between AI-model development in research labs and subsequent clinical deployment and propose solutions. Our report provides guidance on processes which take an imaging AI model from development to clinical implementation in a healthcare institution. We discuss various AI integration points in a clinical Radiology workflow. We also present a taxonomy of Radiology AI use-cases. Through this report, we intend to educate the stakeholders in healthcare and AI (AI researchers, radiologists, imaging informaticists, and regulators) about cross-disciplinary challenges and possible solutions.

This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control--and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current research problems in quantum theory: the quantum mechanical task of maximising the projection of a point on the unitary orbit of an initial state onto a target state C relates to the C-numerical radius of A via maximising the trace function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii) in restricting the dynamics to {\em local} operations on each qubit, i.e. to the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2). Interestingly, the latter then leads to a novel entity, the {\em local} C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither star-shaped nor simply connected in contrast to the conventional C-numerical range. This is shown in the accompanying paper (math-ph/0702005). We present novel applications of the C-numerical range in quantum control assisted by gradient flows on the local unitary group: (1) they serve as powerful tools for deciding whether a quantum interaction can be inverted in time (in a sense generalising Hahn's famous spin echo); (2) they allow for optimising witnesses of quantum entanglement. We conclude by relating the relative C-numerical range to problems of constrained quantum optimisation, for which we also give Lagrange-type gradient flow algorithms.