Unification Framework Research Articles

Reification, Curry-Howard Correspondence, and Didactical Consequences

The roles of languages, processes, and objects in mathematical thinking have led to many theories, yet no consistent big picture has evolved from this. This paper puts forth the hypothesis that the Curry-Howard correspondence from computer science and the theories it is built on provide a unification framework. This correspondence asserts that (formal) proofs and programs (in functional programming languages) do not only have some similarities, but can, at least if formalized in an appropriate way, be mapped to each other by an isomorphism such that proofs are programs and vice versa. Moreover, objects can be realized as function evaluation strategies, and this provides a model of the reification process. The paper explores all this and discusses the didactical relevance; especially, the reification theories are revisited. Computer-based realizations of concepts are used as a tool to show the consistency of ideas and the practicability of concepts.

Quantum Gravity Based on Generalized Thermodynamics

This paper proposes a novel approach and simplified model of Quantum Gravity based on the unification framework of Generalized Thermodynamics which suggests cross-related terms and modified equations of General Relativity and Quantum Mechanics. To address the “background problem”, a metric tensor is introduced into stationary Schrödinger equations via curved coordinates yielding quantum spacetime variation term. Then quantum Lagrangian is added to Einstein-Hilbert functional yielding quantum stress-energy tensor. Obtained from one variational principle, two theories are linked by a common quantum spacetime field. The theory offers some interpretations of the quantum vacuum spacetime fluctuations, zero-point-fields, quantum fields shifting towards high spacetime densities, the quantum nature of spacetime, and black hole singularity.

A Robust Deep Learning Ensemble-Driven Model for Defect and Non-Defect Recognition and Classification Using a Weighted Averaging Sequence-Based Meta-Learning Ensembler.

The need to overcome the challenges of visual inspections conducted by domain experts drives the recent surge in visual inspection research. Typical manual industrial data analysis and inspection for defects conducted by trained personnel are expensive, time-consuming, and characterized by mistakes. Thus, an efficient intelligent-driven model is needed to eliminate or minimize the challenges of defect identification and elimination in processes to the barest minimum. This paper presents a robust method for recognizing and classifying defects in industrial products using a deep-learning architectural ensemble approach integrated with a weighted sequence meta-learning unification framework. In the proposed method, a unique base model is constructed and fused together with other co-learning pretrained models using a sequence-driven meta-learning ensembler that aggregates the best features learned from the various contributing models for better and superior performance. During experimentation in the study, different publicly available industrial product datasets consisting of the defect and non-defect samples were used to train, validate, and test the introduced model, with remarkable results obtained that demonstrate the viability of the proposed method in tackling the challenges of the manual visual inspection approach.

Generalized Simultaneous Localization and Mapping (G-SLAM) as unification framework for natural and artificial intelligences: towards reverse engineering the hippocampal/entorhinal system and principles of high-level cognition.

Simultaneous localization and mapping (SLAM) represents a fundamental problem for autonomous embodied systems, for which the hippocampal/entorhinal system (H/E-S) has been optimized over the course of evolution. We have developed a biologically-inspired SLAM architecture based on latent variable generative modeling within the Free Energy Principle and Active Inference (FEP-AI) framework, which affords flexible navigation and planning in mobile robots. We have primarily focused on attempting to reverse engineer H/E-S “design” properties, but here we consider ways in which SLAM principles from robotics may help us better understand nervous systems and emergent minds. After reviewing LatentSLAM and notable features of this control architecture, we consider how the H/E-S may realize these functional properties not only for physical navigation, but also with respect to high-level cognition understood as generalized simultaneous localization and mapping (G-SLAM). We focus on loop-closure, graph-relaxation, and node duplication as particularly impactful architectural features, suggesting these computational phenomena may contribute to understanding cognitive insight (as proto-causal-inference), accommodation (as integration into existing schemas), and assimilation (as category formation). All these operations can similarly be describable in terms of structure/category learning on multiple levels of abstraction. However, here we adopt an ecological rationality perspective, framing H/E-S functions as orchestrating SLAM processes within both concrete and abstract hypothesis spaces. In this navigation/search process, adaptive cognitive equilibration between assimilation and accommodation involves balancing tradeoffs between exploration and exploitation; this dynamic equilibrium may be near optimally realized in FEP-AI, wherein control systems governed by expected free energy objective functions naturally balance model simplicity and accuracy. With respect to structure learning, such a balance would involve constructing models and categories that are neither too inclusive nor exclusive. We propose these (generalized) SLAM phenomena may represent some of the most impactful sources of variation in cognition both within and between individuals, suggesting that modulators of H/E-S functioning may potentially illuminate their adaptive significances as fundamental cybernetic control parameters. Finally, we discuss how understanding H/E-S contributions to G-SLAM may provide a unifying framework for high-level cognition and its potential realization in artificial intelligences.

Using C++ to Calculate SO(10) Tensor Couplings

Model building in SO(10), which is the leading grand unification framework, often involves large Higgs representations and their couplings. Explicit calculations of such couplings is a multi-step process that involves laborious calculations that are time consuming and error prone, an issue which only grows as the complexity of the coupling increases. Therefore, there exists an opportunity to leverage the abilities of computer software in order to algorithmically perform these calculations on demand. This paper outlines the details of such software, implemented in C++ using in-built libraries. The software is capable of accepting invariant couplings involving an arbitrary number of SO(10) Higgs tensors, each having up to five indices. The output is then produced in LaTeX, so that it is universally readable and sufficiently expressive. Through the use of this software, SO(10) coupling analysis can be performed in a way that minimizes calculation time, eliminates errors, and allows for experimentation with couplings that have not been computed before in the literature. Furthermore, this software can be expanded in the future to account for similar Higgs–Spinor coupling analysis, or extended to include further SO(N) invariant couplings.

Addressing the RD(*) anomalies with an S1 leptoquark from SO(10) grand unification

Motivated by the $R_{D^{(*)}}$ anomalies, we investigate an $\mathrm{SO}(10)$ grand unification scenario where a charge $-1/3$ scalar leptoquark ($S_1$) remains as the only new physics candidate at the TeV scale. This leptoquark along with the Standard Model (SM) Higgs doublet originates from the same 10-dimensional real scalar multiplet in the $\mathrm{SO}(10)$ grand unification framework taking its mass close to the electroweak scale. We explicitly show how the gauge coupling unification is achieved with only one intermediate symmetry-breaking scale at which the Pati-Salam gauge group is broken into the SM group. We investigate the phenomenological implications of our scenario and show that an $S_1$ with a specific Yukawa texture can explain the $R_{D^{(*)}}$ anomalies. We perform a multiparameter scan considering the relevant flavour constraints on $R_{D^{(*)}}$, $F_L{(D^*)}$, $P_\tau(D^*)$ and $R_{K^{(*)}}^{\nu\nu}$ as well as the constraint coming from the $Z\to\tau\tau$ decay and the latest $\tau\tau$ resonance search data at the LHC. Our analysis shows that a single leptoquark solution to the observed $R_{D^{(*)}}$ anomalies with $S_1$ is still a viable solution.

Triplet leptogenesis, type-II seesaw dominance, intrinsic dark matter, vacuum stability and proton decay in minimal SO(10) breakings

We implement type-II seesaw dominance for neutrino mass and baryogenesis through heavy scalar triplet leptogenesis in a class of minimal non-supersymmetric SO(10) models where matter parity as stabilising discrete symmetry as well as WIMP dark matter (DM) candidates are intrinsic predictions of the GUT symmetry. We also find modifications of relevant CP-asymmetry formulas in such models. Baryon asymmetry of the universe as solutions of Boltzmann equations is further shown to be realized for both normal and inverted mass orderings in concordance with cosmological bound and best fit values of the neutrino oscillation data including θ23 in the second octant and large values of leptonic Dirac CP-phases. Type-II seesaw dominance is at first successfully implemented in two cases of spontaneous SO(10) breakings through SU(5) route where the presence of only one non-standard Higgs scalar of intermediate mass ∼ 109−1010 GeV achieves unification. Lower values of the SU(5) unification scales ∼ 1015 GeV are predicted to bring proton lifetimes to the accessible ranges of Super-Kamiokande and Hyper-Kamiokande experiments. Our prediction of WIMP DM relic density in each model is due to a ∼ \U0001d4aa (1) TeV mass matter-parity odd real scalar singlet (⊂ 16H ⊂ SO(10)) verifiable by LUX and XENON1T experiments. This DM is also noted to resolve the vacuum stability issue of the standard scalar potential. When applied to the unification framework of M. Frigerio and T. Hambye, in addition to the minimal fermionic triplet DM solution of 2.7 TeV, our mechanism of type-II seesaw dominance and triplet leptogenesis is also found to make an alternative prediction of the triplet fermion plus the real scalar singlet DM near the TeV scale.

Baryon-dark matter coincidence in mirrored unification

About 80\% of the mass of the present Universe is made up of the unknown (dark matter), while the rest is made up of ordinary matter. It is a very intriguing question why the {\it mass} densities of dark matter and ordinary matter (mainly baryons) are close to each other. It may be hinting the identity of dark matter and furthermore structure of a dark sector. A mirrored world provides a natural explanation to this puzzle. On the other hand, if mirror-symmetry breaking scale is low, it tends to cause cosmological problems. In this letter, we propose a mirrored unification framework, which breaks mirror-symmetry at the grand unified scale, but still addresses the puzzle. The dark matter mass is strongly related with the dynamical scale of QCD, which explains the closeness of the dark matter and baryon masses. Intermediate-energy portal interactions share the generated asymmetry between the visible and dark sectors. Furthermore, our framework is safe from cosmological issues by providing low-energy portal interactions to release the superfluous entropy of the dark sector into the visible sector.

Selfie retoucher: subject-oriented self-portrait enhancement

Sharing self-portraits starts trending nowadays with the boom of social networks and the rise of smartphones. However, limited by the hardware capabilities, self-portraits taken by the front cameras of portable media devices usually face quality problems such as an incomplete field of view and poor lighting style. In our paper, we introduce a selfie retoucher which enhances a self-portrait with the help of N supporting photos that share the same scene and similar shooting time. With the extra information brought by the supporting photos, a lager field of view and a better lighting style can be achieved. To accomplish this, we propose a novel subject-oriented self-portrait enhancement method with a cascaded illumination unification and photos registration framework. Based on the correspondences extracted from the input 1+N photos, our method estimates and updates the illumination and registration coefficients in a cascaded manner. Moreover, a subject-oriented enhancement algorithm is proposed to enhance the face of the photographer in the self-portrait. We adopt a face-specific illumination correction process over the self-portrait to further improve the visual quality of the subject. After the enhancement, we globally fuse the aligned photos by a Markov Random Field based optimization method. During the fusion, a body map is additionally derived from the subject for guidance. Experimental results demonstrate that the proposed method achieves high-quality results in this novel application scenario.

Duality Occurrences: Physical Origin of Wave Functions

The quantum mystery began with the probabilistic interpretation of the wave function. However, this usefulness is definitive in Quantum Mechanics while the suspense continues. The present paper aims to investigate the origin of such a mystery. Hence, considering a relativistic charged particle in quantum vacuum, it appeared that: (i) from a classical association, this electromagnetismself-consistent derives from the usual wave function, which corresponds to the scalar nature in addition to the vector one. (ii) Such duplicity is only justifiable when the related gauge fields describe fermions, in accordance with the previous theory of duality field-matter. This occurrence then corresponds to the appearance of bosons at cell intersections in vacuum lattice, whatever is the field. (iii) From the related gauge couplings, the scalar function must have an unknown vector companion. Both appear as originating the related conservation laws on one side. On the other side, specific variations of the field front would explain their physical origin. (iv) Moreover, both define an original gauge field to which that of law conservation is sensible. (v) Due to definition validity in any reference system, their possible quantization should lead to that of scalar and vector fields of stationary states. At last, the results highlight the connection between waves and fields associable to any object, emphasizing the field unification framework.

A Ternary Unification Framework for Optimizing TCAM-Based Packet Classification Systems

Packet classification is the key mechanism for enabling many networking and security services. Ternary content addressable memory (TCAM) has been the industrial standard for implementing high-speed packet classification because of its constant classification time. However, TCAM chips have small capacity, high power consumption, high heat generation, and large area-size. This paper focuses on the TCAM-based classifier compression problem: given a classifier $C$ , we want to construct the smallest possible list of TCAM entries $T$ that implement $C$ . In this paper, we propose the ternary unification framework (TUF) for this compression problem and three concrete compression algorithms within this framework. The framework allows us to find more optimization opportunities and design new TCAM-based classifier compression algorithms. Our experimental results show that the TUF can speed up the prior algorithm TCAM Razor by 20 times or more and leads to new algorithms that improve compression performance over prior algorithms by an average of 13.7% on our largest real-life classifiers. The experimental results show that our algorithms can improve both the runtime and the compression ratio over prior work.

Renormalizable SU(5) completions of a Zee-type neutrino mass model

We explore the potential of a selected model of radiative neutrino masses to be implemented in a renormalizable SU(5) unification framework. The Zee-type model under consideration uncovers the SU(5) representations in which the new fields are embedded and which may contain also other light states leading to the unification of gauge couplings. We perform an exhaustive search which reveals specific patterns of new states and demonstrate that such patterns are consistent with a general choice of relevant scalar potential. It turns out that all of the specific scenarios which lead to successful unification include the colored scalars testable at the LHC.

Leptoquark mechanism of neutrino masses within the grand unification framework

We demonstrate the viability of the one-loop neutrino mass mechanism within the framework of grand unification when the loop particles comprise scalar leptoquarks (LQs) and quarks of the matching electric charge. This mechanism can be implemented in both supersymmetric and non-supersymmetric models and requires the presence of at least one LQ pair. The appropriate pairs for the neutrino mass generation via the up-type and down-type quark loops are S_3–R_2 and S_{1,,3}–tilde{R}_2, respectively. We consider two distinct regimes for the LQ masses in our analysis. The first regime calls for very heavy LQs in the loop. It can be naturally realized with the S_{1,,3}–tilde{R}_2 scenarios when the LQ masses are roughly between 10^{12} and 5 times 10^{13} GeV. These lower and upper bounds originate from experimental limits on partial proton decay lifetimes and perturbativity constraints, respectively. Second regime corresponds to the collider accessible LQs in the neutrino mass loop. That option is viable for the S_3–tilde{R}_2 scenario in the models of unification that we discuss. If one furthermore assumes the presence of the type II see-saw mechanism there is an additional contribution from the S_3–R_2 scenario that needs to be taken into account beside the type II see-saw contribution itself. We provide a complete list of renormalizable operators that yield necessary mixing of all aforementioned LQ pairs using the language of SU(5). We furthermore discuss several possible embeddings of this mechanism in SU(5) and SO(10) gauge groups.

LHC Probes of TeV-Scale Scalars in SO(10) Grand Unification

We investigate the possibility of TeV-scale scalars as low energy remnants arising in the nonsupersymmetric SO(10) grand unification framework where the field content is minimal. We consider a scenario where the SO(10) gauge symmetry is broken into the gauge symmetry of the Standard Model (SM) through multiple stages of symmetry breaking, and a colored and hypercharged scalar χ picks a TeV-scale mass in the process. The last stage of the symmetry breaking occurs at the TeV-scale where the left-right symmetry, that is, SU(2)L⊗SU(2)R⊗U(1)B-L⊗SU(3)C, is broken into that of the SM by a singlet scalar field S of mass MS~1 TeV, which is a component of an SU(2)R-triplet scalar field, acquiring a TeV-scale vacuum expectation value. For the LHC phenomenology, we consider a scenario where S is produced via gluon-gluon fusion through loop interactions with χ and also decays to a pair of SM gauge bosons through χ in the loop. We find that the parameter space is heavily constrained from the latest LHC data. We use a multivariate analysis to estimate the LHC discovery reach of S into the diphoton channel.

An analysis ofB−L=−2operators from matter-Higgs interactions in a class of supersymmetricSO(10)models

Recently interest in GUT baryogenesis has been resurrected due to the observation that B-violating dimension seven operators that arise in grand unified theories that also violate B-L produce baryon asymmetry that cannot be wiped out by sphaleron processes. While a general analysis of such higher dimensional operators from a bottom up approach exists in the literature, a full analysis of them derived from grand unification does not exist. In this work we present a complete analysis of B-L=-2 operators within a realistic SO(10) grand unification where the doublet-triplet splitting is automatic via a missing partner mechanism. Specifically we compute all allowed dimension five, dimension seven and dimension nine operators arising from matter-Higgs interactions. The relative strength of all the allowed B-L=-2 operators is given. Such interactions are useful in the study of neutrino masses, baryogenesis, proton decay and $n-\bar n$ oscillations within a common realistic grand unification framework.

Beltrami state in black-hole accretion disk: A magnetofluid approach

Using the magnetofluid unification framework, we show that the accretion disk plasma (embedded in the background geometry of a black hole) can relax to a class of states known as the Beltrami-Bernoulli (BB) equilibria. Modeling the disk plasma as a Hall magnetohydrodynamics (MHD) system, we find that the space-time curvature can significantly alter the magnetic (velocity) decay rates as we move away from the compact object; the velocity profiles in BB states, for example, deviate substantially from the predicted corresponding geodesic velocity profiles. These departures imply a rich interplay of plasma dynamics and general relativity revealed by examining the corresponding Bernoulli condition representing "homogeneity" of total energy. The relaxed states have their origin in the constraints provided by the two helicity invariants of Hall MHD. These helicities conspire to introduce an oscillatory length scale into the system that is strongly influenced by relativistic and thermal effects.

From Godunov to a unified hybridized discontinuous Galerkin framework for partial differential equations

By revisiting the basic Godunov approach for system of linear hyperbolic Partial Differential Equations (PDEs) we show that it is hybridizable. As such, it is a natural recipe for us to constructively and systematically establish a unified hybridized discontinuous Galerkin (HDG) framework for a large class of PDEs including those of Friedrichs' type. The unification is fourfold. First, it provides a single constructive procedure to devise HDG schemes for elliptic, parabolic, hyperbolic, and mixed-type PDEs. The key that we exploit is the fact that, for many PDEs, irrespective of their type, the first order form is a hyperbolic system. Second, it reveals the nature of the trace unknowns as the upwind states. Third, it provides a parameter-free HDG framework, and hence eliminating the “usual complaint” that HDG is a parameter-dependent method. Fourth, it allows us to rediscover most existing HDG methods and furthermore discover new ones.We apply the proposed unified framework to three different PDEs: the convection–diffusion–reaction equation, the Maxwell equation in frequency domain, and the Stokes equation. The purpose is to present a step-by-step construction of various HDG methods, including the most economic ones with least trace unknowns, by exploiting the particular structure of the underlying PDEs. The well-posedness of the resulting HDG schemes, i.e. the existence and uniqueness of the HDG solutions, is proved. The well-posedness result is also extended and proved for abstract Friedrichs' systems. We also discuss variants of the proposed unified framework and extend them to the popular Lax–Friedrichs flux and to nonlinear PDEs. Numerical results for transport equation, convection–diffusion equation, compressible Euler equation, and shallow water equation are presented to support the unification framework.

A neuronal gamma oscillatory signature during morphological unification in the left occipitotemporal junction.

Morphology is the aspect of language concerned with the internal structure of words. In the past decades, a large body of masked priming (behavioral and neuroimaging) data has suggested that the visual word recognition system automatically decomposes any morphologically complex word into a stem and its constituent morphemes. Yet the reliance of morphology on other reading processes (e.g., orthography and semantics), as well as its underlying neuronal mechanisms are yet to be determined. In the current magnetoencephalography study, we addressed morphology from the perspective of the unification framework, that is, by applying the Hold/Release paradigm, morphological unification was simulated via the assembly of internal morphemic units into a whole word. Trials representing real words were divided into words with a transparent (true) or a nontransparent (pseudo) morphological relationship. Morphological unification of truly suffixed words was faster and more accurate and additionally enhanced induced oscillations in the narrow gamma band (60-85 Hz, 260-440 ms) in the left posterior occipitotemporal junction. This neural signature could not be explained by a mere automatic lexical processing (i.e., stem perception), but more likely it related to a semantic access step during the morphological unification process. By demonstrating the validity of unification at the morphological level, this study contributes to the vast empirical evidence on unification across other language processes. Furthermore, we point out that morphological unification relies on the retrieval of lexical semantic associations via induced gamma band oscillations in a cerebral hub region for visual word form processing.

SUGRA Grand Unification, LHC and dark matter

A brief review is given of recent developments related to the Higgs signal and its implications for supersymmetry in the supergravity grand unification framework. The Higgs data indicates that the allowed parameter space largely lies on Focal Curves and Focal Surfaces of the Hyperbolic Branch of radiative breaking of the electroweak symmetry where TeV size scalars naturally arise. The high mass of the Higgs leads to a more precise prediction for the allowed range of the spin independent neutralino–proton cross–section which is encouraging for the detection of dark matter in future experiments with greater sensitivity. Also discussed is the status of grand unification and a natural solution to breaking the GUT group at one scale and resolving the doublet–triplet problem. It is shown that the cosmic coincidence can be compatible within a supersymmetric framework in a muticomponent dark matter picture with one component charged under B – L while the other component is the conventional supersymmetric dark matter candidate, the neutralino.

Minimally flavored colored scalar in $ \overline{B}\to {D^{{\left( * \right)}}}\tau \overline{\nu} $ and the mass matrices constraints

The presence of a colored scalar that is a weak doublet with fractional electric charges of $|Q|=2/3$ and $|Q|=5/3$ with mass below 1,TeV can provide an explanation of the observed branching ratios in $B \to D^{(*)} \tau \bar \nu$ decays. The required combination of scalar and tensor operators in the effective Hamiltonian for $b \to c \tau \bar \nu$ is generated through the $t$-channel exchange. We focus on a scenario with a minimal set of Yukawa couplings that can address a semitauonic puzzle and show that its resolution puts a nontrivial bound on the product of the scalar couplings to $\bar \tau b$ and $\bar c \nu$. We also derive additional constraints posed by $Z \to b\bar b$, muon magnetic moment, lepton flavor violating decays $\mu \to e \gamma$, $\tau \to \mu \gamma$, $\tau \to e \gamma$, and $\tau$ electric dipole moment. The minimal set of Yukawa couplings is not only compatible with the mass generation in an SU(5) unification framework, a natural environment for colored scalars, but specifies all matter mixing parameters except for one angle in the up-type quark sector. We accordingly spell out predictions for the proton decay signatures through gauge boson exchange and show that $p \rightarrow \pi^0 e^+$ is suppressed with respect to $p \rightarrow K^+ \bar{\nu}$ and even $p \rightarrow K^0 e^+$ in some parts of available parameter space. Impact of the colored scalar embedding in 45-dimensional representation of SU(5) on low-energy phenomenology is also presented. Finally, we make predictions for rare top and charm decays where presence of this scalar can be tested independently.