Discrete Set Research Articles

Identification of multi-valued treatment effects with unobserved heterogeneity

In this paper, we establish sufficient conditions for identifying treatment effects on continuous outcomes in endogenous and multi-valued discrete treatment settings with unobserved heterogeneity. We employ the monotonicity assumption for multi-valued discrete treatments and instruments, and our identification condition has a clear economic interpretation. In addition, we identify the local treatment effects in multi-valued treatment settings and derive closed-form expressions of the identified treatment effects. We provide examples to illustrate the usefulness of our result.

The conformal sector of Quantum Einstein Gravity beyond the local potential approximation

The anomalous scaling of Newton's constant around the Reuter fixed point is dynamically computed using the functional flow equation approach. Specifically, we thoroughly analyze the flow of the most general conformally reduced Einstein-Hilbert action. Our findings reveal that, due to the distinctive nature of gravity, the anomalous dimension η of the Newton's constant cannot be constrained to have one single value: the ultraviolet critical manifold is characterized by a line of fixed points (g⁎(η),λ⁎(η)), with a discrete (infinite) set of eigenoperators associated to each fixed point. More specifically, we find three ranges of η corresponding to different properties of both fixed points and eigenoperators and, in particular, for the range η<ηc≈0.96 the ultraviolet critical manifolds has finite dimensionality.

A novel approach for multi-stage investment decisions and dynamic variations in medium-term energy planning for multi-energy carriers community

So far, energy planning methods faced several challenges in achieving a proper assessment due to the extreme variability of input conditions. To considerably decrease the computational efforts in achieving solutions, most of the analyses reported in the scientific literature assume constant costs and demand over the entire planning horizon in a typical year. However, results might not be perfectly aligned with real ones because of the incapability of some models to address several aspects like energy demand/production variability, energy and technology costs, efficiency degradation, and use of different energy carriers. This paper proposes a novel methodology that optimises both the long-term planning and short-term scheduling decisions in the management of a multi-energy carries community by means of a Mixed Integer Linear Programming model that also considers the modular design of technologies (e.g., technological devices selection from a discrete set of variants). Such a model has been applied to the case study of a University campus in Italy, whose historical demand data were used for its energy planning with a time horizon of 30 years. Three scenarios have been analysed: (i) the Business As Usual, (ii) the Sector-coupling scenario, and, finally, (iii) the Hydrogen deployment one. The results are obtained under different energy scenarios, showing the effectiveness of the methodology in dealing with multi-investment stages at different planning levels in a reasonable computational time. In particular, they showed that deploying more sustainable technologies would increase the cost of the electricity (between 43%–89%), while reducing other energy carriers’ cost (about 60%) and lowering all energy carriers’ carbon footprint (between 50%–80%). From a long-term perspective, (i) the use of sector-coupling technologies is beneficial from both economic and environmental points of view, and ii) dynamic variations of some parameters can strongly affect the deployment of high-cost technologies to be installed beyond 2030.

Finite Control Set Model Predictive Control (FCS-MPC) for Enhancing the Performance of a Single-Phase Inverter in a Renewable Energy System (RES)

A single-phase five-level T-type topology has been investigated in this article. This topology has emerged as a viable option for renewable energy systems (RES) due to its inherent benefits. The finite control set model predictive control (FCS-MPC) strategy has been implemented to this topology in order to improve the performance and overall reliability of the system. This control strategy empowers the inverter to predict future behavior based on a discrete set of control signals, enabling precise modulation and high-speed response to system dynamics. In the realm of RES, integration of FCS-MPC with multilevel inverters (MLIs) holds great potential to enhance energy conversion efficiency, grid integration, and overall system reliability. The article is structured to present an overview of the evolving landscape of power electronic systems, and the advantages of FCS-MPC. This paper provides a comprehensive analysis of the FCS-MPC control strategy applied to the single-phase five-level T-type topology. The study covers various aspects including the theoretical framework, hardware development, and experimental evaluation. It is obvious from the analysis that this inverter topology is reliable. Several redundant states make it fault-tolerant which helps in maintaining the output voltage at the same level even in the fault conditions. Additionally, the results show that the output load voltage is maintained at the same level irrespective of load change. Also, output load voltage has maintained the high-quality sinusoidal characteristics as the total harmonic distortion (THD) is very low. With all these features, this system is suitable within the framework of RES.

The self-coordination mean-variance strategy in continuous time

The dynamic mean-variance portfolio selection problem is time inconsistent. In the literature, scholars try to derive the pre-committed strategy, the time consistent strategy and the self-coordination strategy. The pre-committed strategy only concern the global investment interest of the investor. The time consistent strategy only concerns the local investment interests of the investor, while the self-coordination strategy balances between the global investment interest and local investment interests of the investor. However, the self-coordination strategy is only studied for the discrete time mean-variance setting. We study the self-coordination strategy for the continuous time mean-variance setting in this paper. With the help of mean-field reformulation, we derive the analytical self-coordination mean-variance strategy and show that the pre-committed strategy and time consistent strategy are special cases of the self-coordination strategy.

GRAPHICAL AND ANALYTICAL DEFINITION OF PARAMETRIC CURVES IN EXPLICIT FORM

The aim of the work is to establish the relationship between graphical and analytical methods of solving problems on the example of the definition of parametric curves in explicit form. The idea is to represent the system of parametric equations of a plane curve in the space of Otxy coordinate system as a system of two projections of the curve on a complex Monge drawing. Then the desired curve can be obtained explicitly as a discrete set of points on the profile plane of projections in the Otxy coordinate system. If we consider the system of curve projections as a single curve in three-dimensional space Otxy, then this curve can be flat and spatial. For planar curves located in a partial position plane, it is easy to make the transition from parametric setting of the curve to an explicit form due to the linear relationship between one of the variables (x or y) and the parameter t. If the curve in the Otxy coordinate system belongs to the general position plane, we can use the projection plane replacement method to transform it to a projecting position. This allows a linear relationship to be established between one of the variables and a parameter to obtain the equation of the curve in explicit form, followed by an inverse transformation of the planes of projections. Mathematically, replacing the plane of projections is equivalent to replacing the coordinate system and reduces it to a rotation around the origin of the coordinates. Formulas for transforming the coordinate system, taking into account the peculiarities of using Monge's complex drawing and for determining the angle of rotation of the coordinate system are given.

Scenario-Based Robust Optimization for Two-Stage Decision Making Under Binary Uncertainty

This paper addresses problems of two-stage optimization under binary uncertainty. We define a scenario-based robust optimization (ScRO) formulation that combines principles of stochastic optimization (by constructing probabilistic scenarios) and robust optimization (by protecting against adversarial perturbations within discrete uncertainty sets). To solve it, we develop a sparse row generation algorithm that iterates between a master problem (which provides a lower bound based on minimal uncertainty sets) and a history-based subproblem (which generates an upper bound and updates minimal uncertainty sets). We generate scenarios and uncertainty sets from element-wise probabilities using a deviation likelihood method or from historical samples using a sample clustering approach. Using public data sets, results suggest that (i) our ScRO formulation outperforms benchmarks based on deterministic, stochastic, and robust optimization; (ii) our deviation likelihood and sample clustering approaches outperform scenario generation baselines; and (iii) our sparse row generation algorithm outperforms off-the-shelf implementation and state-of-the-art cutting plane benchmarks. An application to a real-world ambulance dispatch case study suggests that the proposed modeling and algorithmic approach can reduce the number of late responses by more than 25%. Funding: K. Wang’s research was supported by the National Natural Science Foundation of China [Grants 72322002, 52221005, and 52220105001]

Bers’ simultaneous uniformization and the intersection of Poincaré holonomy varieties

We consider the space of ordered pairs of distinct {mathbb{C}{mathrm{P}}}^{1}-structures on Riemann surfaces (of any orientations) which have identical holonomy, so that the quasi-Fuchsian space is identified with a connected component of this space. This space holomorphically maps to the product of the Teichmüller spaces minus its diagonal.In this paper, we prove that this mapping is a complete local branched covering map. As a corollary, we reprove Bers’ simultaneous uniformization theorem without any quasi-conformal deformation theory. Our main theorem is that the intersection of arbitrary two Poincaré holonomy varieties (operatorname{SL}_{2}mathbb{C}-opers) is a non-empty discrete set, which is closely related to the mapping.

Attractor dynamics with activity-dependent plasticity capture human working memory across time scales

Most cognitive functions require the brain to maintain immediately preceding stimuli in working memory. Here, using a human working memory task with multiple delays, we test the hypothesis that working memories are stored in a discrete set of stable neuronal activity configurations called attractors. We show that while discrete attractor dynamics can approximate working memory on a single time scale, they fail to generalize across multiple timescales. This failure occurs because at longer delay intervals the responses contain more information about the stimuli than can be stored in a discrete attractor model. We present a modeling approach that combines discrete attractor dynamics with activity-dependent plasticity. This model successfully generalizes across all timescales and correctly predicts intertrial interactions. Thus, our findings suggest that discrete attractor dynamics are insufficient to model working memory and that activity-dependent plasticity improves durability of information storage in attractor systems.

An algorithm for the design of optimal finite wordlength FIR filters

In practical FIR digital filter applications it is often necessary to represent the filter coefficients with a finite number of bits. The finite wordlength coefficient restriction reduces the filter quality and increases the filter deviation. This increase can be reduced substantially if the optimal finite wordlength coefficients are used. Computing these coefficients is more difficult and can be slow. It was shown before that the computation time can be significantly reduced with the help of a lower bound on the deviation increase. Derivation of a new algorithm that uses a much better lower bound is the purpose of this paper. We consider the general case of a length N filter with a discrete set of allowable real coefficients and demonstrate the effectiveness of the new algorithm on a set of filter design cases. The results show that this algorithm reduces the computation times up to 3 times when compared with the previously best results.

Transcriptome analysis of Apis mellifera antennae reveals molecular divergence underlying the division of labour in worker bees.

The olfactory system plays a fundamental role in mediating insect behaviour. Worker bees exhibit an age-dependent division of labour, performing discrete sets of behaviours throughout their lifespan. The behavioural states of bees rely on their sense of the environment and chemical communication via their olfactory system, the antennae. However, the olfactory adaptation mechanism of worker bees during their behavioural development remains unclear. In this study, we conducted a comprehensive and quantitative analysis of antennal gene expression in the Apis mellifera of newly emerged workers, nurses, foragers and defenders using RNA-seq. We found that the antenna tissues of honey bees continued developing after transformation from newly emerged workers to adults. Additionally, we identified differentially expressed genes associated with bee development and division of labour. We validated that major royal jelly protein genes are highly and specifically expressed in nurse honey bee workers. Furthermore, we identified and validated significant alternative splicing events correlated with the development and division of labour. These findings provide a comprehensive transcriptome profile and a new perspective on the molecular mechanisms that may underlie the worker honey bee division of labour.

Nested spheroidal figures of equilibrium − IV. On heterogeneous configurations

ABSTRACT The theory of nested figures of equilibrium, expanded in Papers I and II, is investigated in the limit where the number of layers of the rotating body is infinite, enabling to reach full heterogeneity. In the asymptotic process, the discrete set of equations becomes a differential equation for the rotation rate. In the special case of rigid rotation (from centre to surface), we are led to an integro-differential equation (IDE) linking the ellipticity of isopycnic surfaces to the equatorial mass-density profile. In contrast with most studies, these equations are not restricted to small flattenings, but are valid for fast rotators as well. We use numerical solutions obtained from the self-consistent-field method to validate this approach. At small ellipticities (slow rotation), we fully recover Clairaut’s equation. Comparisons with Chandrasekhar’s perturbative approach and with Roberts’ work based on virial equations are successful. We derive a criterion to characterize the transition from slow to fast rotators. The treatment of heterogeneous structures containing mass-density jumps is proposed through a modified IDE.

Mechanical vibration patterns elicit behavioral transitions and habituation in crawling Drosophila larvae.

How animals respond to repeatedly applied stimuli, and how animals respond to mechanical stimuli in particular, are important questions in behavioral neuroscience. We study adaptation to repeated mechanical agitation using the Drosophila larva. Vertical vibration stimuli elicit a discrete set of responses in crawling larvae: continuation, pause, turn, and reversal. Through high-throughput larva tracking, we characterize how the likelihood of each response depends on vibration intensity and on the timing of repeated vibration pulses. By examining transitions between behavioral states at the population and individual levels, we investigate how the animals habituate to the stimulus patterns. We identify time constants associated with desensitization to prolonged vibration, with re-sensitization during removal of a stimulus, and additional layers of habituation that operate in the overall response. Known memory-deficient mutants exhibit distinct behavior profiles and habituation time constants. An analogous simple electrical circuit suggests possible neural and molecular processes behind adaptive behavior.

Growth Kinetics of Random Sequential Adsorption Packings Built of Two-Dimensional Shapes with Discrete Orientations

We studied random sequential adsorption packings constructed from rectangles, ellipses, and discorectangles, where the orientations of constituent shapes were picked from discrete sets of values with varying spacing. It allowed us to monitor the transition between the two edge cases: the parallel alignment and the arbitrary, continuous orientation of the shapes within the packing. The packings were generated numerically. Apart from determining the kinetics of packing growth in low- and high-density regimes, we analyzed the results in terms of packing density and probed the microstructural properties using the density autocorrelation function.

Weighted Axelrod model: Different but similar

The Axelrod model is a cellular automaton which can be used to describe the emergence and development of cultural domains, where culture is represented by a fixed number of cultural features taking a discrete set of possible values (traits). The Axelrod model is based on two sociological phenomena: homophily (a tendency for individuals to form bonds with people similar to themselves) and social influence (the way how individuals change their behavior due to social pressure). However, the Axelrod model does not take into account the fact that cultural attributes may have different significance for a given individual. This is a limitation in the context of how the model reflects mechanisms driving the evolution of real societies. The study aims to modify the Axelrod model by giving individual features different weights that have a decisive impact on the possibility of aligning cultural traits between (interacting) individuals. The comparison of the results obtained for the classic Axelrod model and its modified version shows that introduced weights have a significant impact on the course of the system development, in particular, increasing the final fragmentation of the system and increasing the time needed to reach the final state.

HLA3DB: comprehensive annotation of peptide/HLA complexes enables blind structure prediction of T cell epitopes

The class I proteins of the major histocompatibility complex (MHC-I) display epitopic peptides derived from endogenous proteins on the cell surface for immune surveillance. Accurate modeling of peptides bound to the human MHC, HLA, has been mired by conformational diversity of the central peptide residues, which are critical for recognition by T cell receptors. Here, analysis of X-ray crystal structures within our curated database (HLA3DB) shows that pHLA complexes encompassing multiple HLA allotypes present a discrete set of peptide backbone conformations. Leveraging these backbones, we employ a regression model trained on terms of a physically relevant energy function to develop a comparative modeling approach for nonamer pHLA structures named RepPred. Our method outperforms the top pHLA modeling approach by up to 19% in structural accuracy, and consistently predicts blind targets not included in our training set. Insights from our work may be applied towards predicting antigen immunogenicity, and receptor cross-reactivity.

A novel discrete adjoint-based level set topology optimization method in B-spline space

A novel discrete adjoint-based level set topology optimization method in B-spline space

A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations

In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner. We first derive continuous energy estimates, and then proceed to the discrete setting. We formulate the discrete approximation using high-order finite difference methods on summation-by-parts form and implement the boundary conditions weakly using the simultaneous approximation term method. By applying the discrete energy method and imitating the continuous analysis, the discrete estimate that resembles the continuous counterpart is obtained proving stability. We also show that these newly derived boundary conditions removes the singularities associated with the null-space of the nonlinear discrete spatial operator. Numerical experiments that verifies the high-order accuracy of the scheme and coincides with the theoretical results are presented. The numerical results are compared with the well-known Blasius similarity solution as well as that resulting from the solution of the incompressible Navier–Stokes equations.

Approximation of holomorphic Legendrian curves with jet-interpolation

We prove several interpolation results for holomorphic Legendrian curves lying in an odd dimensional complex Euclidean space with the standard contact structure. In particular, we show that an arbitrary countable set of points in C2n+1 lies on an injectively immersed isotropic surface with a prescribed complex structure. If the set has no accumulation points, the surface may be taken properly embedded. We also prove a Carleman-type theorem for holomorphic Legendrian curves with interpolation. Namely, a Legendrian curve, defined on a certain type of unbounded closed set in a given open Riemann surface R, may be approximated in the C0-topology by an entire Legendrian curve with prescribed finite-order Taylor polynomials at a closed discrete set of points in R. Under suitable conditions, the approximating map may be made into a proper embedding.

Almost Everywhere Convergence Questions of Series of Translates of Non-Negative Functions

This survey paper is based on a talk given at the 44th Summer Symposium in Real Analysis in Paris. This line of research was initiated by a question of Haight and Weizsäker concerning almost everywhere convergence properties of series of the form $\sum_{n=1}^{{\infty}}f(nx)$. A more general, additive version of this problem is the following: Suppose $\Lambda$ is a discrete infinite set of nonnegative real numbers. We say that $ {\Lambda}$ is of type 1 if the series $s(x)=\sum_{\lambda\in\Lambda}f(x+\lambda)$ satisfies a zero-one law. This means that for any non-negative measurable $f: \mathbb R\to [0,+ {\infty})$ either the convergence set $C(f, {\Lambda})=\{x: s(x)<+ {\infty} \}= \mathbb R$ modulo sets of Lebesgue zero, or its complement the divergence set $D(f, {\Lambda})=\{x: s(x)=+ {\infty} \}= \mathbb R$ modulo sets of measure zero. If $ {\Lambda}$ is not of type 1 we say that $ {\Lambda}$ is of type 2. The exact characterization of type $1$ and type $2$ sets is still not known. The part of the paper discussing results concerning this question is based on several joint papers written at the beginning with J-P. Kahane and D. Mauldin, later with B. Hanson, B. Maga and G. Vértesy. Apart from results from the above project we also cover historic background, other related results and open questions.