This work presents an efficient algorithmic framework for real-time identification, classification, and evaluation of human physiotherapy exercises using mobile devices. The proposed method interprets a kinetic movement as a sequence of static poses, which are estimated from camera input using a pose-estimation neural network. Extracted body keypoints are transformed into trigonometric angle-based features and classified with lightweight supervised models to generate frame-level pose predictions and accuracy scores. To recognize full exercise movements and detect deviations from prescribed patterns, we employ a dynamic-programming scheme based on a modified Levenshtein distance algorithm, enabling robust sequence matching and localization of inaccuracies. The system operates entirely on the client side, ensuring scalability and real-time performance. Experimental evaluation demonstrates the effectiveness of the methodology and highlights its applicability to remote physiotherapy supervision and m-health applications.
This survey provides an exposition of a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods, which have recently been applied to address several challenging problems in statistical inference successfully. Topics including polynomial approximation, polynomial interpolation and majorization, moment space and positive polynomials, orthogonal polynomials and Gaussian quadrature are discussed, with their major probabilistic and statistical applications in property estimation on large domains and learning mixture models. These techniques provide useful tools not only for the design of highly practical algorithms with provable optimality, but also for establishing the fundamental limits of the inference problems through the method of moment matching. The effectiveness of the polynomial method is demonstrated in concrete problems such as entropy and support size estimation, distinct elements problem, and learning Gaussian mixture models.
Generative Social Agents (GSAs) are increasingly impacting human users through persuasive means. On the one hand, they might motivate users to pursue personal goals, such as healthier lifestyles. On the other hand, they are associated with potential risks like manipulation and deception, which are induced by limited control over probabilistic agent outputs. However, as GSAs manifest communicative patterns based on available knowledge, their behavior may be regulated through their access to such knowledge. Following this approach, we explored persuasive ChatGPT-generated messages in the context of human-robot physiotherapy motivation. We did so by comparing ChatGPT-generated responses to predefined inputs from a hypothetical physiotherapy patient. In Study 1, we qualitatively analyzed 13 ChatGPT-generated dialogue scripts with varying knowledge configurations regarding persuasive message characteristics. In Study 2, third-party observers (N = 27) rated a selection of these dialogues in terms of the agent's expressiveness, assertiveness, and persuasiveness. Our findings indicate that LLM-based GSAs can adapt assertive and expressive personality traits - significantly enhancing percei
We present a general logical framework for reasoning about agents' cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory including the concepts of knowledge, belief, strong belief, conditional belief, desire, conditional desire, strong desire and preference. We also present two extensions of the logic, one by the notion of choice and the other by dynamic operators for belief change and desire change, and we apply the former to the analysis of single-stage games under incomplete information. We provide sound and complete axiomatizations for the basic logic and for its two extensions. The paper is under consideration in Theory and Practice of Logic Programming (TPLP).
Probabilistic Answer Set Programming under the credal semantics (PASP) extends Answer Set Programming with probabilistic facts that represent uncertain information. The probabilistic facts are discrete with Bernoulli distributions. However, several real-world scenarios require a combination of both discrete and continuous random variables. In this paper, we extend the PASP framework to support continuous random variables and propose Hybrid Probabilistic Answer Set Programming (HPASP). Moreover, we discuss, implement, and assess the performance of two exact algorithms based on projected answer set enumeration and knowledge compilation and two approximate algorithms based on sampling. Empirical results, also in line with known theoretical results, show that exact inference is feasible only for small instances, but knowledge compilation has a huge positive impact on the performance. Sampling allows handling larger instances, but sometimes requires an increasing amount of memory. Under consideration in Theory and Practice of Logic Programming (TPLP).
We propose a unified methodology to input non-linear views from any number of users in fully general non-normal markets, and perform, among others, stress-testing, scenario analysis, and ranking allocation. We walk the reader through the theory and we detail an extremely efficient algorithm to easily implement this methodology under fully general assumptions. As it turns out, no repricing is ever necessary, hence the methodology can be readily applied to books with complex derivatives. We also present an analytical solution, useful for benchmarking, which per se generalizes notable previous results. Code illustrating this methodology in practice is available at http://www.mathworks.com/matlabcentral/fileexchange/21307
Involutive category theory provides a flexible framework to describe involutive structures on algebraic objects, such as anti-linear involutions on complex vector spaces. Motivated by the prominent role of involutions in quantum (field) theory, we develop the involutive analogs of colored operads and their algebras, named colored $\ast$-operads and $\ast$-algebras. Central to the definition of colored $\ast$-operads is the involutive monoidal category of symmetric sequences, which we obtain from a general product-exponential $2$-adjunction whose right adjoint forms involutive functor categories. For $\ast$-algebras over $\ast$-operads we obtain involutive analogs of the usual change of color and operad adjunctions. As an application, we turn the colored operads for algebraic quantum field theory into colored $\ast$-operads. The simplest instance is the associative $\ast$-operad, whose $\ast$-algebras are unital and associative $\ast$-algebras.
Approximation Fixpoint Theory (AFT) is an algebraic framework designed to study the semantics of non-monotonic logics. Despite its success, AFT is not readily applicable to higher-order definitions. To solve such an issue, we devise a formal mathematical framework employing concepts drawn from Category Theory. In particular, we make use of the notion of Cartesian closed category to inductively construct higher-order approximation spaces while preserving the structures necessary for the correct application of AFT. We show that this novel theoretical approach extends standard AFT to a higher-order environment, and generalizes the AFT setting of arXiv:1804.08335 . Under consideration in Theory and Practice of Logic Programming (TPLP).
We construct a version of Beilinson's regulator as a map of sheaves of commutative ring spectra and use it to define a multiplicative variant of differential algebraic K-theory. We use this theory to give an interpretation of Bloch's construction of K_3-classes and the relation with dilogarithms. Furthermore, we provide a relation to Arakelov theory via the arithmetic degree of metrized line bundles, and we give a proof of the formality of the algebraic K-theory of number rings.
This work concentrates on the study of inverse determinant sums, which arise from the union bound on the error probability, as a tool for designing and analyzing algebraic space-time block codes. A general framework to study these sums is established, and the connection between asymptotic growth of inverse determinant sums and the diversity-multiplexing gain trade-off is investigated. It is proven that the growth of the inverse determinant sum of a division algebra-based space-time code is completely determined by the growth of the unit group. This reduces the inverse determinant sum analysis to studying certain asymptotic integrals in Lie groups. Using recent methods from ergodic theory, a complete classification of the inverse determinant sums of the most well known algebraic space-time codes is provided. The approach reveals an interesting and tight relation between diversity-multiplexing gain trade-off and point counting in Lie groups.
We study a relation between the Drinfeld modules and the even dimensional noncommutative tori. A non-abelian class field theory is developed based on this relation. Explicit generators of the Galois extensions are constructed.
Solving a decision theory problem usually involves finding the actions, among a set of possible ones, which optimize the expected reward, possibly accounting for the uncertainty of the environment. In this paper, we introduce the possibility to encode decision theory problems with Probabilistic Answer Set Programming under the credal semantics via decision atoms and utility attributes. To solve the task we propose an algorithm based on three layers of Algebraic Model Counting, that we test on several synthetic datasets against an algorithm that adopts answer set enumeration. Empirical results show that our algorithm can manage non trivial instances of programs in a reasonable amount of time. Under consideration in Theory and Practice of Logic Programming (TPLP).
We show that the F-theory dual of the heterotic string with unbroken Spin(32)/Z_2 symmetry in eight dimensions can be described in terms of the same polyhedron that can also encode unbroken E_8\times E_8 symmetry. By considering particular compactifications with this K3 surface as a fiber, we can reproduce the recently found `record gauge group' in six dimensions and obtain a new `record gauge group' in four dimensions. Our observations relate to the toric diagram for the intersection of components of degenerate fibers and our definition of these objects, which we call `tops', is more general than an earlier definition by Candelas and Font.
In this paper we show how prescritive type checking and constraint solving can be combined to increase automation during software verification. We do so by defining a type system and implementing a typechecker for {log} (read `setlog'), a Constraint Logic Programming (CLP) language and satisfiability solver based on set theory. Hence, we proceed as follows: a) a type system for {log} is defined; b) the constraint solver is proved to be safe w.r.t. the type system; c) the implementation of a concrete typechecker is presented; d) the integration of type checking and set constraint solving to increase automation during software verification is discussed; and f) two industrial-strength case studies are presented where this combination is used with very good results. Under consideration in Theory and Practice of Logic Programming (TPLP)
Social robots offer a promising solution for autonomously guiding patients through physiotherapy exercise sessions, but effective deployment requires advanced decision-making to adapt to patient needs. A key challenge is the scarcity of patient behavior data for developing robust policies. To address this, we engaged 33 expert healthcare practitioners as patient proxies, using their interactions with our robot to inform a patient behavior model capable of generating exercise performance metrics and subjective scores on perceived exertion. We trained a reinforcement learning-based policy in simulation, demonstrating that it can adapt exercise instructions to individual exertion tolerances and fluctuating performance, while also being applicable to patients at different recovery stages with varying exercise plans.
The unitary representation theory of locally compact contraction groups and their semi-direct products with $\mathbb{Z}$ is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this article provides a stepping stone towards a solution to this problem. In particular, we determine new examples of type I and non-type-I groups in this class, and we completely classify the irreducible unitary representations of the torsion-free groups, which are shown to be type I. When these groups are totally disconnected, they admit a faithful action by automorphisms on an infinite locally-finite regular tree; this work thus provides new examples of automorphism groups of regular trees with interesting representation theory, adding to recent work on this topic.
Thom Frühwirth presented a short, elegant and efficient Prolog program for the n queens problem. However the program may be seen as rather tricky and one may not be convinced about its correctness. This paper explains the program in a declarative way, and provides proofs of its correctness and completeness. The specification and the proofs are declarative, i.e. they abstract from any operational semantics. The specification is approximate, it is unnecessary to describe the program's semantics exactly. Despite the program works on non-ground terms, this work employs the standard semantics, based on logical consequence and Herbrand interpretations. Another purpose of the paper is to present an example of precise declarative reasoning about the semantics of a logic program. Under consideration in Theory and Practice of Logic Programming (TPLP).
The functional Schrodinger picture formulation of quantum field theory and the variational Gaussian approximation method based on the formulation are briefly reviewed. After presenting recent attempts to improve the variational approximation, we introduce a new systematic method based on the background field method, which enables one to compute the order-by-order correction terms to the Gaussian approximation of the effective action.
Objective: Participation in a physical therapy program is considered one of the greatest predictors of successful conservative management of common shoulder disorders. However, adherence to these protocols is often poor and typically worse for unsupervised home exercise programs. Currently, there are limited tools available for objective measurement of adherence in the home setting. The goal of this study was to develop and evaluate the potential for performing home shoulder physiotherapy monitoring using a commercial smartwatch. Approach: Twenty healthy adult subjects with no prior shoulder disorders performed seven exercises from an evidence-based rotator cuff physiotherapy protocol, while 6-axis inertial sensor data was collected from the active extremity. Within an activity recognition chain (ARC) framework, four supervised learning algorithms were trained and optimized to classify the exercises: k-nearest neighbor (k-NN), random forest (RF), support vector machine classifier (SVC), and a convolutional recurrent neural network (CRNN). Algorithm performance was evaluated using 5-fold cross-validation stratified first temporally and then by subject. Main Results: Categorical clas
In this paper, we introduce the action language C-MT (Mind Transition Language). It is built on top of answer set programming (ASP) and transition systems to represent how human mental states evolve in response to sequences of observable actions. Drawing on well-established psychological theories, such as the Appraisal Theory of Emotion, we formalize mental states, such as emotions, as multi-dimensional configurations. With the objective to address the need for controlled agent behaviors and to restrict unwanted mental side-effects of actions, we extend the language with a novel causal rule, forbids to cause, along with expressions specialized for mental state dynamics, which enables the modeling of principles for valid transitions between mental states. These principles of mental change are translated into transition constraints, and properties of invariance, which are rigorously evaluated using transition systems in terms of so-called trajectories. This enables controlled reasoning about the dynamic evolution of human mental states. Furthermore, the framework supports the comparison of different dynamics of change by analyzing trajectories that adhere to different psychological p