Lattice Approach Research Articles

A new lattice approach for risk-minimization hedging under generalized autoregressive conditional heteroskedasticity models

This paper explores the calculation of risk-minimization hedging strategies, specifically local and global risk minimization strategies for contingent claims under affine and non-affine GARCH models with the known closed forms of its first four moments across times under the physical measure. A unified and efficient willow tree method is introduced for various GARCH models. Unlike methods that provide option values and hedging ratios solely at the inception time, the proposed willow tree method generates a comprehensive table of option values and hedging ratios at each discrete time step across possible asset prices. Additionally, the method showcases robust performance in hedging at lower frequencies than the underlying asset’s modeling frequency (e.g., weekly or monthly hedging using a daily GARCH model). Lastly, the willow tree method outperforms the Monte Carlo method, offering greater efficiency, accuracy, and flexibility in solving risk-minimization hedging problems.

Utilizing the lattice method to enhance multiplication automaticity in Grade 4 Pupils

This study introduced a new method to help students who struggle with multiplying multiple digits. This study examined the effect of the lattice approach on multiplication automaticity among Grade 4 students at Cateel Central Elementary School during the school year 2023-2024. Utilizing a quasi-experimental methodology, the study compared two intact groups: a control group with 22 respondents taught using traditional multiplication methods, and an experimental group with 21 respondents taught using the lattice method. Pre-test results indicated that neither the control nor the experimental group met the expectations set by the K to 12 grading system, with grade percentages of 65.68 and 67.22, respectively. Statistical analysis showed no significant difference between the pre-test scores of the two groups, suggesting a similar initial level of multiplication proficiency. Post-test results, however, revealed a significant improvement in the experimental group's performance, with a grade percentage of 84.77 compared to the control group's 74.70. The statistical analysis confirmed this difference as significant, with a t-value of -3.383 and a p-value of 0.002. The findings demonstrate the superior efficacy of the lattice method over traditional teaching methods in enhancing multiplication skills among Grade 4 students.

Optimization of Flexural Strength of Sawdust Ash Blended Geopolymer Concrete

release of greenhouse gases linked to the manufacture of cement. Geopolymer as a binder for making concrete consists of two (2) main components; (1) the alkaline liquid consisting of sodium or potassium silicate and sodium or potassium hydroxide and (2) source material of geological origin or by-products rich in silica and alumina. The combination proportions utilised in this investigation were formulated utilising Scheffe's (5,2) basic lattice mix design approach with the intent to create the trial mix and the control mix. A total of thirty (30) geopolymers concrete sample mixes were made in the laboratory, with fifteen samples for trial mixes and fifteen mixtures for control mixes. These mixtures were used to appraise the performance of the sawdust ash geopolymer concrete in term of its flexural strength property. The study used sawdust ash as the source material and investigation revealed that subjecting sawdust ash to pyrolysis without oxygen has a notable impact on the pozzolanic characteristics of the constituent. Consequently, this also affects the flexural qualities of the concrete. Furthermore, it has been shown that softwood sawdust exhibits superior pozzolanic properties when compared to hardwood sawdust. The study revealed that the optimum flexural strength of sawdust ash blended geopolymer concrete is 3.3002 MPa and the corresponding mix deign obtained. Computer programs were created using Matlab and used for the optimization and prediction of the flexural strength of sawdust ash based geopolymer concrete.

Neural networks for emergent behavior in biological microstructures

PurposeThis paper develops a neural network surrogate model based on a discrete lattice approach to investigate the influence of complex microstructures on the emergent behavior of biological networks.Design/methodology/approachThe adaptability of network-forming organisms, such as, slime molds, relies on fluid-to-solid state transitions and dynamic behaviors at the level of the discrete microstructure, which continuum modeling methods struggle to capture effectively. To address this challenge, we present an optimized approach that combines lattice spring modeling with machine learning to capture dynamic behavior and develop nonlinear constitutive relationships.FindingsThis integrated approach allows us to predict the dynamic response of biological materials with heterogeneous microstructures, overcoming the limitations of conventional trial-and-error lattice design. The study investigates the microstructural behavior of biological materials using a neural network-based surrogate model. The results indicate that our surrogate model is effective in capturing the behavior of discrete lattice microstructures in biological materials.Research limitations/implicationsThe combination of numerical simulations and machine learning endows simulations of the slime mold Physarum polycephalum with a more accurate description of its emergent behavior and offers a pathway for the development of more effective lattice structures across a wide range of applications.Originality/valueThe novelty of this research lies in integrating lattice spring modeling and machine learning to explore the dynamic behavior of biological materials. This combined approach surpasses conventional methods, providing a more holistic and accurate representation of emergent behaviors in organisms.

Multiresolution lattice-based support generation for additive manufacturing

The generation of support for 3D models toward 3D printing is a highly challenging task that is of great need in many additive manufacturing processes. In this work, we explore the use of multiresolution geometric lattices to generate support with controlled contact locations. That is, with bounds on the maximal distance between adjacent local support points. A variety of end-user controls over the synthesized support are provided, such as the angular slopes in the model that are provided with support and/or controls on the dimensions and sizes of the support lattice tiles. These controls are augmented with the option of an automated optimization via a direct link to analysis. We demonstrate this proposed lattice approach for support synthesis on several 3D models of different types.

AN ANN MODEL FOR PREDICTING SLUMP OF CONCRETE CONTAINING CRUSHED GLASS AND NATURAL GRAVEL

This study modelled the slump of concrete containing crushed glass and Bida Natural Gravel (BNG) based on deep learning algorithm using the MATLAB neural network toolbox. A total of 240 (150mm × 150mm × 150mm) cubes were cast from 80 mixes generated randomly using Scheffe’s simplex lattice approach. Slump was measured for each of the experimental points of fresh concrete before filling in the moulds. The resulting batch for each mix was used as input data while the laboratory results for slump was used as output data for the ANN-model. Hence a shallow multilayer supervised Neural Network was developed to model these data. The developed model would be able to predict concrete slump containing 0% - 25% crushed glass as partial replacement for fine aggregate, water- cement ratio ranging from 0.45 – 0.65 and concrete grade M15 – M25. The architecture of the network contained 6 input parameters: water to cement ratio, water, cement, sand, crushed glass and BNG, 20 neurons in the hidden layer and slump in the outer layer. The adequacy of the developed model was measured using Mean Square Error (MSE) and Correlation Coefficient (R). Results showed that 6:20:1 model architecture for slump model had an MSE values for training, validation and testing as: 1.84e-2, 5.81e-3, 3.64e-3, 1.73e-3 respectively. Regression values for training, validation and testing are: 79%, 94%, 96% and 79%. The study concluded that a shallow multilayer Neural Network architecture with 20 neurons in the hidden layer is sufficient for predicting concrete slump.

Toward QCD on quantum computer: orbifold lattice approach

We propose an orbifold lattice formulation of QCD suitable for quantum simulations. We show explicitly how to encode gauge degrees of freedom into qubits using noncompact variables, and how to write down a simple truncated Hamiltonian in the coordinate basis. We show that SU(3) gauge group variables and quarks in the fundamental representation can be implemented straightforwardly on qubits, for arbitrary truncation of the gauge manifold.

Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov chains: A Banach lattice approach

We establish the existence and uniqueness of quasi-stationary and quasi-ergodic measures for almost surely absorbed discrete-time Markov chains under weak conditions. We obtain our results by exploiting Banach lattice properties of transition functions under natural regularity assumptions.

An overview of lattice results for parton distribution functions

Following a ground-breaking proposal by Ji [Phys. Rev. Lett. 110, 262002 (2013)], numerical simulations of Quantum Chromo Dynamics (QCD) on a Euclidean lattice have provided new, valuable information on the structure of hadrons. In this talk, we briefly review the lattice approach to the reconstruction of parton densities, highlighting the connection between lattice observables and parton densities, with a focus on theoretical issues. Since parton distributions are extracted from lattice data by solving an inverse problem, we discuss some of the difficulties that affect these determinations and how they can be formulated in a Bayesian framework.

An opportunity cost model to value deferral options

This study discusses a real options valuation approach based on the familiar opportunity cost concept. After demonstrating the equivalence of the opportunity model to the binomial lattice approach of Cox, Ross, and Rubinstein (CRR), we discuss its attributes through simple numerical examples. In contrast to the CRR approach, the transparency of the opportunity model provides an intuitive and economical baseline for managerial discussions and decision-making. We focus on the opportunity costs inherently embedded in the real options value (ROV); therefore, our study is distinct from most other studies, which consider them as the exogenous input to the ROV.

Enhancing Hydrogen Evolution Reaction Activity of Palladium Catalyst by Immobilization on MXene Nanosheets.

Efficient catalysts with minimal content of catalytically active noble metals are essential for the transition to the clean hydrogen economy. Catalyst supports that can immobilize and stabilize catalytic nanoparticles and facilitate the supply of electrons and reactants to the catalysts are needed. Being hydrophilic and more conductive compared with carbons, MXenes have shown promise as catalyst supports. However, the controlled assembly of their 2D sheets creates a challenge. This study established a lattice engineering approach to regulate the assembly of exfoliated Ti3C2Tx MXene nanosheets with guest cations of various sizes. The enlargement of guest cations led to a decreased interlayer interaction of MXene lamellae and increased surface accessibility, allowing intercalation of Pd nanoparticles. Stabilization of Pd nanoparticles between interlayer-expanded MXene nanosheets improved their electrocatalytic activity. The Pd-immobilized K+-intercalated MXene nanosheets (PdKMX) demonstrated exceptional electrocatalytic performance for the hydrogen evolution reaction with the lowest overpotential of 72 mV (@10 mA cm-2) and the highest turnover frequency of 1.122 s-1 (@ an overpotential of 100 mV), which were superior to those of the state-of-the-art Pd nanoparticle-based electrocatalysts. Weakening of the interlayer interaction during self-assembly with K+ ions led to fewer layers in lamellae and expansion of the MXene in the c direction during Pd anchoring, providing numerous surface-active sites and promoting mass transport. In situ spectroscopic analysis suggests that the effective interfacial electron injection from the Pd nanoparticles strongly immobilized on interlayer-expanded PdKMX may be responsible for the improved electrocatalytic performance.

Fair valuations of insurance policies under multiple risk factors: A flexible lattice approach

AbstractWe propose a flexible lattice model to evaluate the fair value of insurance contracts embedding both financial and actuarial risk factors. Flexibility relies on the ability of the model to manage different specifications of the correlated processes governing interest rate, mortality, and fund dynamics, thus allowing the insurer to make the most appropriate choices. The model is also able to handle additional guarantees like a surrender opportunity for which explicit formulae are not available being it similar to an American derivative. The model discretizes mortality and interest rate dynamics through two different binomial lattices and then combines them into a bivariate tree characterized by the presence of four branches for each node. The probability of each branch is defined to replicate the correlation affecting the two processes. The bivariate model is useful to compute the value of survival zero coupon bond. When adding another source of risk, such as the fund dynamics for evaluating fund-linked insurance products, we model it through a bivariate tree that captures the influence of the interest rate on its drift term. Then, the mortality risk is embedded by defining a trivariate tree presenting eight branches emanating from each node with probabilities defined in order to capture the correlations of the processes. Extensive numerical experiments assess the model accuracy by considering some stylized policies, but the model application is not limited to them being it able to manage different contract specifications.

A novel iterative detection method based on a lattice reduction-aided algorithm for MIMO OFDM systems

The lattice reduction-aided algorithm has received broad attention from researchers since it operates as a maximum likelihood receiver with better system performance for multiple-input multiple-output orthogonal frequency division multiplexing systems and contains a full diversity. A novel iterative detection algorithm canceling parallel iterations that employ the lattice reduction-aided approach is proposed. Soft information is exchanged through the detector itself. Its iteration occurs inside the detector, which reduces much of the exchange cost between the multiple-input multiple-output orthogonal frequency division multiplexing detector and the turbo decoder. Since the parallel interference cancellation algorithm is constrained by the accuracy of the initial value of the detection, it is easy to form error propagation after several iterations. Due to the lattice reduction-aided algorithm, its performance is approximated with the maximum likelihood algorithm. Therefore, the lattice reduction-aided algorithm is introduced into the parallel interference cancellation algorithm to make its detection algorithm more accurate and overcome the effect of error propagation in the manuscript. Simulation results indicate that the proposed algorithm leads to an improvement of 0.8–2 dB when the bit error rate is set to 10–4 when compared to other algorithms.

Thermodynamics of the Glassy Polymer State: Equilibrium and Non-Equilibrium Aspects.

This work examines, first, the non-equilibrium character of the glassy state of polymer systems and its significance in the development of novel materials for important technological applications. Subsequently, it summarizes the essentials of the generalized lattice fluid approach for the description of this highly complex non-equilibrium behavior with an approximate and simple, yet analytically powerful formalism. The working equations are derived in a straightforward and consistent manner by clearly defining the universal and specific variables needed to describe the discussed properties. The role of the non-random distribution of molecular species and free volume in the glassy system is also examined, as is the role of strong specific interactions, such as hydrogen-bonding networks. This work also reports examples of applications in a variety of representative systems, including glass densification, retrograde vitrification, increase in glass-transition temperature in hydrogen-bonded polymer mixtures, and hysteresis phenomena in sorption-desorption from glassy polymer matrices.

TT¯ Deformation: A Lattice Approach

Integrable quantum field theories can be regularized on the lattice while preserving integrability. The resulting theories on the lattice are integrable lattice models. A prototype of such a regularization is the correspondence between a sine-Gordon model and a six-vertex model on a light-cone lattice. We propose an integrable deformation of the light-cone lattice model such that in the continuum limit we obtain the TT¯-deformed sine-Gordon model. Under this deformation, the cut-off momentum becomes energy dependent and the underlying Yang–Baxter integrability is preserved. Therefore, this deformation is integrable but non-local: similar to the TT¯ deformation of quantum field theory.

Simplicial graviton from selfdual Ashtekar variables

In perturbative gravity, it is straight-forward to characterize the two local degrees of freedom of the gravitational field in terms of a mode expansion of the linearized perturbation. In the non-perturbative regime, we are in a more difficult position. It is not at all obvious how to construct Dirac observables that can separate the gauge orbits. Standard procedures rely on asymptotic boundary conditions or formal Taylor expansions of relational observables. In this paper, we lay out a new non-perturbative lattice approach to tackle the problem in terms of Ashtekar’s self-dual formulation. Starting from a simplicial decomposition of space, we introduce a local kinematical phase space at the lattice sites. At each lattice site, we introduce a set of constraints that replace the generators of the hypersurface deformation algebra in the continuum. We show that the discretized constraints close under the Poisson bracket. The resulting reduced phase space describes two complex physical degrees of freedom representing the two radiative modes at the discretized level. The paper concludes with a discussion of the key open problems ahead and the implications for quantum gravity.

Entanglement Distillation Optimization Using Fuzzy Relations for Quantum State Tomography

Practical entanglement distillation is a critical component in quantum information theory. Entanglement distillation is often utilized for designing quantum computer networks and quantum repeaters. The practical entanglement distillation problem is formulated as a bilevel optimization problem. A fuzzy formulation is introduced to estimate the quantum state (density matrix) from pseudo-likelihood functions (i.e., quantum state tomography). A scale-independent relationship between fuzzy relations in terms of the pseudo-likelihood functions is obtained. The entanglement distillation optimization problem is solved using the combined coupled map lattice and dual annealing approach. Comparative analysis of the results is then conducted against a standard dual annealing algorithmic implementation.

Clinical aspects of spatially fractionated radiation therapy treatments

PurposeTo provide clinical guidance for centers wishing to implement photon spatially fractionated radiation therapy (SFRT) treatments using either a brass grid or volumetric modulated arc therapy (VMAT) lattice approach. MethodsWe describe in detail processes which have been developed over the course of a 3-year period during which our institution treated over 240 SFRT cases. The importance of patient selection, along with aspects of simulation, treatment planning, quality assurance, and treatment delivery are discussed. Illustrative examples involving clinical cases are shown, and we discuss safety implications relevant to the heterogeneous dose distributions. ResultsSFRT can be an effective modality for tumors which are otherwise challenging to manage with conventional radiation therapy techniques or for patients who have limited treatment options. However, SFRT has several aspects which differ drastically from conventional radiation therapy treatments. Therefore, the successful implementation of an SFRT treatment program requires the multidisciplinary expertise and collaboration of physicians, physicists, dosimetrists, and radiation therapists. ConclusionsWe have described methods for patient selection, simulation, treatment planning, quality assurance and delivery of clinical SFRT treatments which were built upon our experience treating a large patient population with both a brass grid and VMAT lattice approach. Preclinical research and patient trials aimed at understanding the mechanism of action are needed to elucidate which patients may benefit most from SFRT, and ultimately expand its use.

Lattice Approach for Option Pricing under Lévy Processes

This article discusses a new lattice approach for pricing options when the underlying asset price process follows the exponential Lévy model. This article proposes a new lattice method that can be applied to a wide range of Lévy processes. Lévy processes include various models, such as Brownian motion, the compound Poisson process, and the infinite intensity jump model with finite and infinite variation. We introduce a versatile algorithm for option pricing in the exponential Lévy process models. Numerical experiments show that the proposed method accurately calculates options prices.

The influence of boundary scattering phase shift on melting behavior of nanoparticles

Based on the Lindemann melting criterion and the lattice dynamical approach, we analytically estimated the melting temperature of nanoparticles with emphasis on the influence of the boundary scattering phase shift parameter α . With the decrease of size, the estimated relation shows that the melting temperature of free standing like nanoparticles will decrease, and the melting temperature of embedded nanoparticles will increase. The increase or decrease of the melting temperature depends on the boundary scattering phase shift parameter. The gradual change of parameter α from − 1 to 1 corresponds to the transition of the surface or environment of nanoparticles from the free boundary condition to the fixed boundary condition. Our analytical estimation qualitatively explains the experimental data, and its predictive capability will help the design of nanoparticles. • Based on the Lindemann criterion, An analytical estimation for size-dependent melting temperature of nanoparticles by lattice dynamical method will be given. • Our theoretical result can fit experimental data of nanoparticles in different environments qualitatively. • A simple boundary scattering phase shift is used to characterize the environment of nanoparticles.