Space Formulation Research Articles

Visualizing Memory Scapes: A Spatio- Affective Study of Select War Memorials of Jammu and Kashmir

The paper through iconographic and spatial dynamics, critically engages with the performative aspect of the select war memorial sites in the erstwhile state of Jammu and Kashmir. While the interdisciplinary study of war memorials in relation to memory and commemorative politics have been studied, its materialistic aesthetics informed through spatial and affective contours remains a burgeoning field of enquiry if not an unexampled one. The study is premised on the photographic field work of the sites envisioned through the cultural geography of war memorials. In approaching war memorial sites as a landscape of memory, we take the position that memory is simultaneously a material and immaterial phenomenon and these cannot be detached from affective and visceral human bonds and their roles in (re-)formulations in space and place. The materialistic aesthetics of memory- memorial continuum are ideated through spatial and affective contours, which, in turn, inform the predominant and everyday experience of grief and bereavement, both imagined and lived. The study dominantly attests its claims through Foucault’s concept of ‘heterotopia’ in relation to commemorative sites. The heterotopic tensions of multiple experiences and belongings are unpacked through both tangible and affective domains ranging from dominant public commemorative sites to parks and shopping complexes.

Joint multizonal transdimensional Bayesian inversion of surface wave dispersion and ellipticity curves for local near-surface imaging

SummaryPhysical properties of near-surface soil and rock layers play a fundamental role in the seismic site effects analysis, being an essential element of seismic hazard assessment. Site-specific mechanical properties (i.e. shear- and compressional-wave velocities and mass density) can be inferred from surface wave dispersion and horizontal-to-vertical or ellipticity data by non-linear inversion techniques. Nevertheless, results typically exhibit significant inherent non-uniqueness as different models may fit the data equally well. Standard optimization inversion techniques minimize data misfit, resulting in a single representative model, rejecting other models providing similar misfit values. An alternative inversion technique can be formulated in the Bayesian framework, where the posterior probability density on the model space is inferred. This paper introduces an inversion approach of surface wave dispersion and ellipticity data based on a novel multizonal transdimensional Bayesian formulation. In particular, we parametrize 1-D layered velocity models by the varying number of Voronoi nuclei, allowing us to treat the number of layers as an unknown parameter of the inverse problem. The chosen parametrization leads to the transdimensional formulation of the model space, sampled by a reversible jump Markov chain Monte Carlo algorithm to provide an ensemble of random samples following the posterior probability density of model parameters. The used type of the sampling algorithm controls a model complexity (i.e. the number of layers) self-adaptively based on the measured data's information content. The method novelty lies in the parsimonious selection of sampling models and in the multizonal formulation of prior assumptions on model parameters, the latter allows including additional site-specific constraints in the inversion. These assumptions may be based on, e.g. stratigraphic logs, standard penetration tests, known water table, and bedrock depth. The multizonal formulation fully preserves the validity of the transdimensional one, as demonstrated analytically. The resultant ensemble of model samples is a discrete approximation of the posterior probability density function of model parameters and associated properties (e.g. VS30, quarter-wavelength average velocity profile and theoretical SH-wave amplification function). Although the ultimate result is the posterior probability density function, some representative models are selected according to data fit and maximum of the posterior probability density function. We first validate our inversion approach based on synthetic tests and then apply it to field data acquired from the active seismic survey and single-station measurements of ambient vibrations at the SENGL seismic station site in central Switzerland.

Finite element-based grasp analysis using contact pressure maps of a robotic gripper

Conventionally, a robotic grasp is represented by point contacts with rigid body description for object and gripper. With these assumptions, the contact forces and moments are considered to act at points, and a grasp wrench space is constructed to determine the stability of the grasp. However, wrench space formulations ensure mechanical equilibrium only; it does not guarantee grasp stability. Moreover, the material properties of object and grippers are not taken into account, as a result of which the underlying deformation and the contact pressure are neglected. In this work, the contact pressure maps of robotic grasps, that accounts for deformability occurring at the gripper-object interface, are used for robotic grasp analysis and database generation. Using a conformable pressure sensing sheet, the contact pressure maps of typical household objects such as cans, bottles and cubes, while grasping and perturbation are measured and explored. Apart from these objects, the contact pressure maps of fruits such as apple and orange, while grasping is also studied. The stability of each grasp is determined based on the contact pressure maps, and a contact area-based metric, $$\pi $$ , is used to identify the most stable grasp. These pressure maps are then used to validate the FE framework designed for robotic grasp analysis. $$\pi $$ obtained from experiments is then compared with that of FE simulation outputs, and it is observed that the relative error between them is less than 4%, which, in turn, demonstrates the efficacy of the proposed framework. As the FE framework is not suited for real-time grasp synthesis due to the computational time involved, we show how to exploit the framework for generating an offline grasp experience database, which can then be deployed for grasp synthesis real-time.

Inertial methods for finding minimum-norm solutions of the split variational inequality problem beyond monotonicity

In solving the split variational inequality problems, very few methods have been considered in the literature and most of these few methods require the underlying operators to be co-coercive. This restrictive co-coercive assumption has been dispensed with in some methods, many of which require a product space formulation of the problem. However, it has been discovered that this product space formulation may cause some potential difficulties during implementation and its approach may not fully exploit the attractive splitting structure of the split variational inequality problem. In this paper, we present two new methods with inertial steps for solving the split variational inequality problems in real Hilbert spaces without any product space formulation. We prove that the sequence generated by these methods converges strongly to a minimum-norm solution of the problem when the operators are pseudomonotone and Lipschitz continuous. Also, we provide several numerical experiments of the proposed methods in comparison with other related methods in the literature.

Covariant phase space and soft factorization in non-Abelian gauge theories

We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity.

Enforcing Sustainable Forest Management Policies: An Assessment of the Institutional Structures for VPA Implementation in Ghana

Public policy formulation in the forestry management space is an essential step in addressing issues of environmental degradation. That notwithstanding, policies will remain mere intents if they are not forged with appropriate structures and institutional underpinnings. This study assesses the institutional and structural mechanisms adopted to foster effective implementation of the Voluntary Partnership Agreement in Ghana. The qualitative case study design was employed to gather data from purposively selected respondents. The study observes that after ratification of the VPA in Ghana, this was forged with subsequent measures to ensure smooth operationalization of same. The structures include a Legality Assurance System (LAS); chain of custody and wood tracking system (GWTS); establishment of a Timber Verification Department to check and verify the legality of all timbers among others. The structures also entail collaborative governance, transparency and accountability measures to ensure operationalization of the VPA requirements. The study observes that where there are multiple, overlapping and independent actors along the value chain, trust and credibility is built such that those in the downstream of the implementation remain very careful and conscientious in their operations and dealings. The study concludes that relevant implementation structures interspersed with actor constellations, and multi-stake holding remain cornerstone of SFM arrangements.

Polarization tensor in de Sitter gauge gravity

The gauge theory of the de Sitter group, [Formula: see text], in the ambient space formalism has been considered in this paper. This method is important to construction of the de Sitter super-conformal gravity and Quantum gravity. [Formula: see text] gauge vector fields are needed which correspond to [Formula: see text] generators of the de Sitter group. Using the gauge-invariant Lagrangian, the field equations of these vector fields have been obtained. The gauge vector field solutions are recalled. By using these solutions, the spin-[Formula: see text] gauge potentials has been constructed. There are two possibilities for presenting this tensor field: rank-[Formula: see text] symmetric and mixed symmetry rank-[Formula: see text] tensor fields. To preserve the conformal transformation, a spin-[Formula: see text] field must be represented by a mixed symmetry rank-[Formula: see text] tensor field, [Formula: see text]. This tensor field has been rewritten in terms of a generalized polarization tensor field and a de Sitter plane wave. This generalized polarization tensor field has been calculated as a combination of vector polarization, [Formula: see text], and tensor polarization of rank-2, [Formula: see text], which can be used in the gravitational wave consideration. There is a certain extent of arbitrariness in the choice of this tensor and we fix it in such a way that, in the limit, [Formula: see text], one obtains the polarization tensor in Minkowski spacetime. It has been shown that under some simple conditions, the spin-[Formula: see text] mixed symmetry rank-[Formula: see text] tensor field can be simultaneously transformed by unitary irreducible representation of de Sitter and conformal groups ([Formula: see text]).

Launch in the pharmaceutical sector - innovation with niche formulations applying lean startUPs models

Research, development and application of entrepreneurship models based on the methodology described by Eric Ries, an entrepreneur and businessman who, after several experiences of failure in startUP project development in Silicon Valley (USA), understood that for his business model works, it had to evolve; firstly, optimizing costs in the product development phase and secondly, concentrating time using a 3-phase wheel: I. Prototype launch II. Collecting customer experience and satisfaction metrics, answering the question “Does it meet the customer's need?” III. Learning and improving the final product adapting it to the experience collected. This business model makes business projects viable in the early stages of development, which must evolve to adapt to the market. Laboratorios Avanceutics is an entrepreneurial project led by María Moreno - Pharmaceutical and CFO, and Jesús Nieva Pharmaceutical and CEO. This project is focused on the formulation, development and manufacture of phytotherapeutics, nutraceuticals and functional supplementation for the pharma sector. Through market research and after cost evaluation, we understood that the investment in both fixed and variable costs at the beginning of the project in Pre-Seed phase, was very high. Therefore, in order to make the project economically viable, we had to look for alternatives that do not increase the financial burden but to optimize it. For this reason, we managed to adapt the Lean StarUP method to the different phases of laboratory development, carrying out a cost optimization that made possible to develop the first formulations to launch on the market. The methodology used in the optimization of resources was applied, adapted, and divided into: Phase 1: Elimination of intermediaries. Focused on research and learning in conducting: market studies, marketing, regulatory and National (Aecosan) and European (Efsa) legislation, graphic design, die-cutting, web design (html - wordpress) for ecommerce development. Phase 2: Stock adaptation, negotiation with supplier laboratories to adapt the minimum purchases to the needs, making consumption agreements. Within the product development methodology, we have subdivided 4 stages that help us to optimize the management of the formulation from its origin, these phases are F.1 discovery, F.2 Pre-formulation, F.3 Development (phase A) and F. 4 Development (phase B) and launch. As a result of the adaptation of this model and of our own research, it has been possible to develop 7 formulations in a short space of time and making the first phases of implementation and market access of the project viable, all within one of the most important and competitiveness sectors such as the pharmaceutical market.

Convergence Rates for the Quantum Central Limit Theorem

Various quantum analogues of the central limit theorem, which is one of the cornerstones of probability theory, are known in the literature. One such analogue, due to Cushen and Hudson, is of particular relevance for quantum optics. It implies that the state in any single output arm of an n-splitter, which is fed with n copies of a centred state rho with finite second moments, converges to the Gaussian state with the same first and second moments as rho . Here we exploit the phase space formalism to carry out a refined analysis of the rate of convergence in this quantum central limit theorem. For instance, we prove that the convergence takes place at a rate mathcal {O}left( n^{-1/2}right) in the Hilbert–Schmidt norm whenever the third moments of rho are finite. Trace norm or relative entropy bounds can be obtained by leveraging the energy boundedness of the state. Via analytical and numerical examples we show that our results are tight in many respects. An extension of our proof techniques to the non-i.i.d. setting is used to analyse a new model of a lossy optical fibre, where a given m-mode state enters a cascade of n beam splitters of equal transmissivities lambda ^{1/n} fed with an arbitrary (but fixed) environment state. Assuming that the latter has finite third moments, and ignoring unitaries, we show that the effective channel converges in diamond norm to a simple thermal attenuator, with a rate mathcal {O}Big (n^{-frac{1}{2(m+1)}}Big ). This allows us to establish bounds on the classical and quantum capacities of the cascade channel. Along the way, we derive several results that may be of independent interest. For example, we prove that any quantum characteristic function chi _rho is uniformly bounded by some eta _rho <1 outside of any neighbourhood of the origin; also, eta _rho can be made to depend only on the energy of the state rho .

Classical simulation of quantum circuits using fewer Gaussian eliminations

A compelling way to quantify the separation between classical and quantum computing is to determine how many $T$-gate magic states, $t$, a classical computer must simulate to calculate the probability of a universal quantum circuit's output. Unfortunately, efforts to determine the minimum number of stabilizer state inner products necessary to decompose $T$-gate magic states (${\ensuremath{\chi}}_{t}$) have proven intractable past $t=7$. By using a phase space formalism based on Wootters' discrete Weyl operator basis over a finite field, we develop an algebraic approach to determining ${\ensuremath{\chi}}_{t}$ for single-Pauli measurements. This allows us to extend the bounds on ${\ensuremath{\chi}}_{t}$ to $t=14$ for qutrits, effectively increasing the space searched by $&gt;{10}^{{10}^{4}}$. Our results show that by using such phase space methods it is possible to validate noisy intermediate-scale quantum circuits of larger size than previously thought possible.

A Practical Fourth Order Finite-Difference Time-Domain Algorithm for the Solution of Maxwell’s Equations

Implementing a practical fourth order accurate in time and second order accurate in space finite difference time domain simulation using MATLAB is the goal of this paper. The formulation presented for the fourth order approximation is simple to integrate into an existing second order accurate in time and second order accurate in space formulation and well-established code. The fourth order formulation has been verified and simulation accuracy is confirmed through the application of radiation from a single and an array of dipole antennas.

Wigner functions in quantum mechanics with a minimum length scale arising from generalized uncertainty principle

In this paper, we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle. We present the phase space formulation of such theories following GUP and show that the Weyl transform and the Wigner function satisfy most of their known properties in standard quantum mechanics. We utilize the generalized Wigner function to calculate the phase space average of the Hamiltonian of a quantum harmonic oscillator satisfying deformed Heisenberg algebra. It is also shown that averages of certain quantum mechanical operators in such theories may restrict the value of the deformation parameter specifying the degree of deformation of Heisenberg algebra. All the results presented are for pure states. The results can be generalized for mixed states.

Most general theory of 3d gravity: covariant phase space, dual diffeomorphisms, and more

We show that the phase space of three-dimensional gravity contains two layers of dualities: between diffeomorphisms and a notion of “dual diffeomorphisms” on the one hand, and between first order curvature and torsion on the other hand. This is most elegantly revealed and understood when studying the most general Lorentz-invariant first order theory in connection and triad variables, described by the so-called Mielke-Baekler Lagrangian. By analyzing the quasi-local symmetries of this theory in the covariant phase space formalism, we show that in each sector of the torsion/curvature duality there exists a well-defined notion of dual diffeomorphism, which furthermore follows uniquely from the Sugawara construction. Together with the usual diffeomorphisms, these duals form at finite distance, without any boundary conditions, and for any sign of the cosmological constant, a centreless double Virasoro algebra which in the flat case reduces to the BMS3 algebra. These algebras can then be centrally-extended via the twisted Sugawara construction. This shows that the celebrated results about asymptotic symmetry algebras are actually generic features of three-dimensional gravity at any finite distance. They are however only revealed when working in first order connection and triad variables, and a priori inaccessible from Chern-Simons theory. As a bonus, we study the second order equations of motion of the Mielke-Baekler model, as well as the on-shell Lagrangian. This reveals the duality between Riemannian metric and teleparallel gravity, and a new candidate theory for three-dimensional massive gravity which we call teleparallel topologically massive gravity.

Spectral Green's-function method in driven open quantum dynamics

A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics that can be described by the Lindblad master equation in Liouville density operator space. The method extends the Hilbert space formalism and provides simple algebraic connections between the driven and non-driven dynamics in the spectral frequency domain. The formalism shows remarkable analogies to the use of Green functions in quantum field theory such as the elementary excitation energies and the Dyson self-energy equation. To demonstrate its potential, we apply the novel method to a coherently driven dissipative ensemble of 2-level systems comprising a single "active" subsystem interacting with $N$ "passive" subsystems -- a generic model with important applications in quantum optics and dynamic nuclear polarization. The novel method dramatically reduces computational cost compared with simulations based on solving the full master equation, thus making it possible to study and optimize many-body correlated states in the physically realistic limit of an arbitrarily large $N$.

A time series approach to player churn and conversion in videogames

Players of a free-to-play game are divided into three main groups: non-paying active users, paying active users and inactive users. A State Space time series approach is then used to model the daily conversion rates between the different groups, i.e., the probability of transitioning from one group to another. This allows, not only for predictions on how these rates are to evolve, but also for a deeper understanding of the impact that in-game planning and calendar effects have. It is also used in this work for the detection of marketing and promotion campaigns about which no information is available. In particular, two different State Space formulations are considered and compared: an Autoregressive Integrated Moving Average process and an Unobserved Components approach, in both cases with a linear regression to explanatory variables. Both yield very close estimations for covariate parameters, producing forecasts with similar performances for most transition rates. While the Unobserved Components approach is more robust and needs less human intervention in regards to model definition, it produces significantly worse forecasts for non-paying user abandonment probability. More critically, it also fails to detect a plausible marketing and promotion campaign scenario.

Quantum Mechanics and Its Evolving Formulations.

In this paper, we discuss the time evolution of the quantum mechanics formalism. Starting from the heroic beginnings of Heisenberg and Schrödinger, we cover successively the rigorous Hilbert space formulation of von Neumann, the practical bra-ket formalism of Dirac, and the more recent rigged Hilbert space approach.

Market Making With Signals Through Deep Reinforcement Learning

Deep reinforcement learning has recently been successfully applied to a plethora of diverse and difficult sequential decision-making tasks, ranging from the Atari games to robotic motion control. Among the foremost such tasks in quantitative finance is the problem of optimal market making. Market making is the process of simultaneously quoting limit orders on both sides of the limit order book of a security with the goal of repeatedly capturing the quoted spread while minimizing the inventory risk. Most of the existing analytical approaches to market making tend to be predicated on a set of strong, naive assumptions, whereas current machine learning-based approaches either resort to crudely discretized quotes or fail to incorporate additional predictive signals. In this paper, we present a novel framework for market making with signals based on model-free deep reinforcement learning, addressing these shortcomings. A new state space formulation incorporating outputs from standalone signal generating units, as well as a novel action space and reward function formulation, are introduced. The framework is underpinned by both ideas from adversarial reinforcement learning and neuroevolution. Experimental results on historical data demonstrate the superior reward-to-risk performance of the proposed framework over several standard market making benchmarks. More specifically, the resulting reinforcement learning agent achieves between 20-30% higher terminal wealth than the benchmarks while being exposed to only around 60% of their inventory risks. Finally, an insight into its policy is provided for the sake of interpretability.

A Whole-Body Control Framework Based on the Operational Space Formulation Under Inequality Constraints via Task-Oriented Optimization

This paper presents practical enhancements of the operational space formulation (OSF) to exploit inequality constraints for whole-body control of a high degree of freedom robot with a floating base and multiple contacts, such as humanoids. A task-oriented optimisation method is developed to obtain a feasible torque resolution solely for task variables based on the OSF, which effectively reduces the number of optimisation variables. Interestingly, the proposed scheme amends assigned tasks on demand of satisfying inequality conditions, while dynamic consistency among contact-constrained tasks is preserved. In addition, we propose an efficient algorithm structure ameliorating real-time control capability which has been a major hurdle to transplant optimisation methods into the OSF-based whole-body control framework. Control performance, the feasibility of the optimised solution, and the computation time of the proposed control framework are verified through realistic dynamic simulations of a humanoid. We also clarify the pros and cons of the proposed method compared with existing optimisation-based ones, which may offer an insight for practical control engineers to select whole-body controllers necessitated from the desired application.

The Operational Space Formulation on Humanoids Considering Joint Stiffness and Bandwidth Limit

As the applications of robots increase, mobility and capability of interaction in unstructured environments have become important. Hence, humanoid robots have been developed to have these capabilities, and recently, compliant motions for safe contact have been studied. The Operational Space Formulation can be an effective method for humanoid robots to realize compliant motion via unified motion and force control. Nevertheless, the implementation of the Operational Space Formulation on humanoid robots has not been successful. One of the challenging issues is low position tracking performance. In this study, a control method for solving this problem is proposed by considering the joint stiffness and joint bandwidth limits. To consider joint stiffness, the Operational Space Formulation was derived using flexible joint robot dynamics. Additionally, an extra torque generation method, which penalizes low performance actuators, is utilized to account for the bandwidth limits. Neither methods requires additional sensors or joint space controllers. Hence, they can be useful for conventional humanoid robots composed of electric motors and gears. By integrating the two methods, the position tracking performance of the Operational Space Formulation on the humanoid robot was significantly improved. The proposed method was demonstrated via position and orientation control experiments using our humanoid robot, TOCABI.

Anomalies in gravitational charge algebras of null boundaries and black hole entropy

We revisit the covariant phase space formalism applied to gravitational theories with null boundaries, utilizing the most general boundary conditions consistent with a fixed null normal. To fix the ambiguity inherent in the Wald-Zoupas definition of quasilocal charges, we propose a new principle, based on holographic reasoning, that the flux be of Dirichlet form. This also produces an expression for the analog of the Brown-York stress tensor on the null surface. Defining the algebra of charges using the Barnich-Troessaert bracket for open subsystems, we give a general formula for the central — or more generally, abelian — extensions that appear in terms of the anomalous transformation of the boundary term in the gravitational action. This anomaly arises from having fixed a frame for the null normal, and we draw parallels between it and the holographic Weyl anomaly that occurs in AdS/CFT. As an application of this formalism, we analyze the near-horizon Virasoro symmetry considered by Haco, Hawking, Perry, and Strominger, and perform a systematic derivation of the fluxes and central charges. Applying the Cardy formula to the result yields an entropy that is twice the Bekenstein-Hawking entropy of the horizon. Motivated by the extended Hilbert space construction, we interpret this in terms of a pair of entangled CFTs associated with edge modes on either side of the bifurcation surface.