Let $C$ be a complex irreducible plane curve that is not the vanishing locus of a modular polynomial. We show that $C$ contains finitely many real algebraic curves whose projection on each coordinate axis is a union of special geodesics.
Creating virtual digital replicas from real-world data unlocks significant potential across domains like gaming and robotics. In this paper, we present DRAWER, a novel framework that converts a video of a static indoor scene into a photorealistic and interactive digital environment. Our approach centers on two main contributions: (i) a reconstruction module based on a dual scene representation that reconstructs the scene with fine-grained geometric details, and (ii) an articulation module that identifies articulation types and hinge positions, reconstructs simulatable shapes and appearances and integrates them into the scene. The resulting virtual environment is photorealistic, interactive, and runs in real time, with compatibility for game engines and robotic simulation platforms. We demonstrate the potential of DRAWER by using it to automatically create an interactive game in Unreal Engine and to enable real-to-sim-to-real transfer for robotics applications.
When cells measure concentrations of chemical signals, they may average multiple measurements over time in order to reduce noise in their measurements. However, when cells are in a environment that changes over time, past measurements may not reflect current conditions - creating a new source of error that trades off against noise in chemical sensing. What statistics in the cell's environment control this tradeoff? What properties of the environment make it variable enough that this tradeoff is relevant? We model a single eukaryotic cell sensing a chemical secreted from bacteria (e.g. folic acid). In this case, the environment changes because the bacteria swim - leading to changes in the true concentration at the cell. We develop analytical calculations and stochastic simulations of sensing in this environment. We find that cells can have a huge variety of optimal sensing strategies, ranging from not time averaging at all, to averaging over an arbitrarily long time, or having a finite optimal averaging time. The factors that primarily control the ideal averaging are the ratio of sensing noise to environmental variation, and the ratio of timescales of sensing to the timescale of environmental variation. Sensing noise depends on the receptor-ligand kinetics, while the environmental variation depends on the density of bacteria and the degradation and diffusion properties of the secreted chemoattractant. Our results suggest that fluctuating environmental concentrations may be a relevant source of noise even in a relatively static environment.
Jan Vykopal, Pavel Seda, Valdemar Švábenský
et al.
Hands-on computing education requires a realistic learning environment that enables students to gain and deepen their skills. Available learning environments, including virtual and physical labs, provide students with real-world computer systems but rarely adapt the learning environment to individual students of various proficiency and background. We designed a unique and novel smart environment for adaptive training of cybersecurity skills. The environment collects a variety of student data to assign a suitable learning path through the training. To enable such adaptiveness, we proposed, developed, and deployed a new tutor model and a training format. We evaluated the learning environment using two different adaptive trainings attended by 114 students of various proficiency. The results show students were assigned tasks with a more appropriate difficulty, which enabled them to successfully complete the training. Students reported that they enjoyed the training, felt the training difficulty was appropriately designed, and would attend more training sessions like these. Instructors can use the environment for teaching any topic involving real-world computer networks and systems because it is not tailored to particular training. We freely released the software along with exemplary training so that other instructors can adopt the innovations in their teaching practice.
We study the chaotic motion of a semi-classical optomechanical system coupled to a non-Markovian environment with a finite correlation time. We show that the non-Markovian environment can significantly enhance chaos, by studying the emergence of chaos using Lyapunov exponent with the changing non-Markovian parameter. It is observed that non-Markovian environment characterized by the Ornstein-Uhlenbeck type noise can modify the generation of chaos with different environmental memory times. As a comparison, the crossover properties from Markov to non-Markovian regimes are also discussed. Our findings indicate that the quantum memory effects on the onset of chaos may become a useful property to be investigated in quantum manipulations and control.
Motivated by geometric Langlands, we initiate a program to study the mirror symmetry between nilpotent orbit closures of a semisimple Lie algebra and those of its Langlands dual. The most interesting case is $B_n$ via $C_n$. Classically, there is a famous Springer duality between special orbits. Therefore, it is natural to speculate that the mirror symmetry we seek may coincide with Springer duality in the context of special orbits. Unfortunately, such a naive statement fails. To remedy the situation, we propose a conjecture which asserts the mirror symmetry for certain parabolic/induced covers of special orbits. Then, we prove the conjecture for Richardson orbits and obtain certain partial results in general. In the process, we reveal some very interesting and yet subtle structures of these finite covers, which are related to Lusztig's canonical quotients of special nilpotent orbits. For example, there is a mysterious asymmetry in the footprint or range of degrees of these finite covers. Finally, we provide two examples to show that the mirror symmetry fails outside the footprint.
We develop an extension of posterior sampling for reinforcement learning (PSRL) that is suited for a continuing agent-environment interface and integrates naturally into agent designs that scale to complex environments. The approach, continuing PSRL, maintains a statistically plausible model of the environment and follows a policy that maximizes expected $γ$-discounted return in that model. At each time, with probability $1-γ$, the model is replaced by a sample from the posterior distribution over environments. For a choice of discount factor that suitably depends on the horizon $T$, we establish an $\tilde{O}(τS \sqrt{A T})$ bound on the Bayesian regret, where $S$ is the number of environment states, $A$ is the number of actions, and $τ$ denotes the reward averaging time, which is a bound on the duration required to accurately estimate the average reward of any policy. Our work is the first to formalize and rigorously analyze the resampling approach with randomized exploration.
Articulation of issues. A number of bases, positions, which previously were recognized as the only correct and irrefutable, served as the foundation of legal regulation of civil relations. But now they do not fully correspond to modern tendencies in the development of civil law science. That is why, today, it should be mentioned about the formation of a new doctrine, which can meet the requirements of the formation and development of the rule-of-law state. In such conditions, it is obvious that the scientific and theoretical study of individual approaches to the allocation of types of servitudes from the standpoint of accounting will contribute to the improvement of civil-law relations, to the formation of a clear and coherent system. At the same time, the variety of scientific views about types of way-leaves constantly encourages the implementation and improvement of scientific research in the field of property rights for someone else’s property. In this context, the issue of the implementation of contractual, inheritance, and land relations for servitudes becomes very important and necessary. Also, another important question is: Are specific legislative approaches to allocation of servitudes on the basis of specific features fixed in legislation or not? Has the legislator stopped only on land and personal servitude? The aim of the article is to study the theoretical and legal possibilities and approaches to the allocation of way-leaves on the basis of specific features from the standpoint of accounting and jurisprudence. Also, another aim is to attract the attention of legal scholars to possible further scientific researches on the introduction of this phenomenon in modern civil legislation of Ukraine. The subject of the study is the individual approaches to the allocation of types of servitudes from the standpoint of accounting. Methodology. The research is based on the analysis of legal acts, which are connected with legal regulation of way-leave relations in Ukraine. On the basis of the comparative legal method of investigation of certain provisions of Ukrainian legislation, the possibilities and limits of the use of types of servitudes in contractual hereditary and land relations are determined. Results of this study have shown that special approaches to the allocation of way-leaves on the basis of specific features in Ukraine are in a real legal vacuum. Such a conclusion is based on the lack of legislative clarification and consolidation of other types of servitudes, which are not connected with the material component. Thus, property rights under the Tax Code of Ukraine are intangible assets, and the provisions of the Civil Code of Ukraine consolidate the material constituent of real rights to someone else’s property. From the standpoint of accounting, we can talk about the presence of intangible servitudes that are associated with the recognition and accounting of intangible assets. If this gap will be solved, then we can talk about the revision of the characteristics of way-leaves, relying on the positions of other branches of law. Practical impact. The idea that certain positions of intangible servitude are contained in national law is rather necessary and expedient. So, we can talk about corporate rights as a person’s rights, the share of which is determined in the statutory fund (property) of a business organization. These rights include the competence to participate in the management of a business entity, obtaining a certain percentage of profits (dividends) of this organization and assets in case of liquidation of it in accordance with the law, as well as other powers provided by law and statutory documents and, for example, the rights to use websites, or aspects of commercial secrecy. Correlation/originality. An analysis of the possible use of other types of way-leaves than those, which are enshrined in civil law in contractual, inheritance, land relations can become the basis for developing the most promising directions for the development of domestic civil law in this area and improving the civil law doctrine.
Maja Zebić Avdičević, Krešimir Košutić, Slaven Dobrović
AbstractThis study investigates the performance of three ultrafiltration membranes, i.e. a submerged polyethylene (PE) hollow fibre membrane, a multibore polyethersulfone (PES) membrane and a tubular multichannel ceramic membrane in the textile mercerization wastewater treatment. Experiments were carried out on two laboratory dead end membranes and on a cross flow membrane set‐up using wastewater with and without the addition of MgCl2 as a coagulant. Investigation into energy consumption was also carried out. According to the obtained results, the submerged membrane could be used as the pretreatment of mercerization wastewater to significantly reduce the amount of suspended solids, to remove organic carbon and to decrease turbidity. The results showed that the tested membranes could be used for the treatment of wastewater from the textile mercerization process in terms of permeate quality. The cross‐flow ultrafiltration consumes far more energy than the dead‐end process.
We study BPS jumping loci, or the subloci in moduli spaces of supersymmetric string vacua where BPS states come into existence discontinuously. This phenomenon is distinct from wall-crossing. We argue that these loci should be thought of as special cycles in the sense of Noether-Lefschetz loci or special Shimura subvarieties, which are indeed examples of BPS jumping loci for certain string compactifications. We use the Hodge-elliptic genus as an informative tool, suggesting that our work can be extended to understand the jumping behavior of motivic Donaldson-Thomas invariants.
We review properties of affine special Kaehler structures focusing on singularities of such structures in the simplest case of real dimension two. We describe all possible isolated singularities and compute the monodromy of the flat symplectic connection, which is a part of a special Kaehler structure, near a singularity. Beside numerous local examples, we construct continuous families of special Kaehler structures with isolated singularities on the projective line.
We prove a formula of the equivariant infinity-adic special L-values of abelian t-modules. This gives function field analogues of the equivariant class number formula. As an application, we calculate the special values of Artin L-functions for Galois representations.