kinematic space
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2021 ◽  
Vol 2021 (11) ◽  
James Drummond ◽  
Jack Foster ◽  
Ömer Gürdoğan ◽  
Chrysostomos Kalousios

Abstract We describe a family of tropical fans related to Grassmannian cluster algebras. These fans are related to the kinematic space of massless scattering processes in a number of ways. For each fan associated to the Grassmannian Gr(k, n) there is a notion of a generalised ϕ3 amplitude and an associated set of scattering equations which further generalise the Gr(k, n) scattering equations that have been recently introduced. Here we focus mostly on the cases related to finite Grassmannian cluster algebras and we explain how face variables for the cluster polytopes are simply related to the scattering equations. For the Grassmannians Gr(4, n) the tropical fans we describe are related to the singularities (or symbol letters) of loop amplitudes in planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We show how each choice of tropical fan leads to a natural class of polylogarithms, generalising the notion of cluster adjacency and we describe how the currently known loop data fit into this classification.

BMC Biology ◽  
2021 ◽  
Vol 19 (1) ◽  
Guillaume Le Goc ◽  
Julie Lafaye ◽  
Sophia Karpenko ◽  
Volker Bormuth ◽  
Raphaël Candelier ◽  

Abstract Background Variability is a hallmark of animal behavior. It contributes to survival by endowing individuals and populations with the capacity to adapt to ever-changing environmental conditions. Intra-individual variability is thought to reflect both endogenous and exogenous modulations of the neural dynamics of the central nervous system. However, how variability is internally regulated and modulated by external cues remains elusive. Here, we address this question by analyzing the statistics of spontaneous exploration of freely swimming zebrafish larvae and by probing how these locomotor patterns are impacted when changing the water temperatures within an ethologically relevant range. Results We show that, for this simple animal model, five short-term kinematic parameters — interbout interval, turn amplitude, travelled distance, turn probability, and orientational flipping rate — together control the long-term exploratory dynamics. We establish that the bath temperature consistently impacts the means of these parameters, but leave their pairwise covariance unchanged. These results indicate that the temperature merely controls the sampling statistics within a well-defined kinematic space delineated by this robust statistical structure. At a given temperature, individual animals explore the behavioral space over a timescale of tens of minutes, suggestive of a slow internal state modulation that could be externally biased through the bath temperature. By combining these various observations into a minimal stochastic model of navigation, we show that this thermal modulation of locomotor kinematics results in a thermophobic behavior, complementing direct gradient-sensing mechanisms. Conclusions This study establishes the existence of a well-defined locomotor space accessible to zebrafish larvae during spontaneous exploration, and quantifies self-generated modulation of locomotor patterns. Intra-individual variability reflects a slow diffusive-like probing of this space by the animal. The bath temperature in turn restricts the sampling statistics to sub-regions, endowing the animal with basic thermophobicity. This study suggests that in zebrafish, as well as in other ectothermic animals, ambient temperature could be used to efficiently manipulate internal states in a simple and ethological way.

2021 ◽  
Vol 2021 (8) ◽  
Suchetan Das ◽  
Bobby Ezhuthachan ◽  
Somnath Porey ◽  
Baishali Roy

Abstract We construct an infinite class of eigenmodes with integer eigenvalues for the Vacuum Modular Hamiltonian of a single interval N in 2d CFT and study some of its interesting properties, which includes its action on OPE blocks as well as its bulk duals. Our analysis suggests that these eigenmodes, like the OPE blocks have a natural description on the so called kinematic space of CFT2 and in particular realize the Virasoro algebra of the theory on this kinematic space. Taken together, our results hints at the possibility of an effective description of the CFT2 in the kinematic space language.

2021 ◽  
Vol 2021 (7) ◽  
Mrunmay Jagadale ◽  
Alok Laddha

Abstract Building on the seminal work of Arkani-Hamed, He, Salvatori and Thomas (AHST) [1] we explore the positive geometry encoding one loop scattering amplitude for quartic scalar interactions. We define a new class of combinatorial polytopes that we call pseudo-accordiohedra whose poset structures are associated to singularities of the one loop integrand associated to scalar quartic interactions. Pseudo-accordiohedra parametrize a family of projective forms on the abstract kinematic space defined by AHST and restriction of these forms to the type-D associahedra can be associated to one-loop integrands for quartic interactions. The restriction (of the projective form) can also be thought of as a canonical top form on certain geometric realisations of pseudo-accordiohedra. Our work explores a large class of geometric realisations of the type-D associahedra which include all the AHST realisations. These realisations are based on the pseudo-triangulation model for type-D cluster algebras discovered by Ceballos and Pilaud [2].

2021 ◽  
Vol 2021 (7) ◽  
Aidan Herderschee

Abstract There is a remarkable connection between the boundary structure of the positive kinematic region and branch points of integrated amplitudes in planar $$ \mathcal{N} $$ N = 4 SYM. A long-standing question has been precisely how algebraic branch points emerge from this picture. We use wall crossing and scattering diagrams to systematically study the boundary structure of the positive kinematic regions associated with MHV amplitudes. The notion of asymptotic chambers in the scattering diagram naturally explains the appearance of algebraic branch points. Furthermore, the scattering diagram construction also motivates a new coordinate system for kinematic space that rationalizes the relations between algebraic letters in the symbol alphabet. As a direct application, we conjecture a complete list of all algebraic letters that could appear in the symbol alphabet of the 8-point MHV amplitude.

2021 ◽  
Vol 2021 (4) ◽  
A. Ramesh Chandra ◽  
Jan de Boer ◽  
Mario Flory ◽  
Michal P. Heller ◽  
Sergio Hörtner ◽  

Abstract We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the gravitational action. The optimal circuit minimizes the gravitational action. This is a generalization of both the “complexity equals volume” conjecture to unoptimized circuits, and path integral optimization to finite cutoffs. Using tools from holographic $$ T\overline{T} $$ T T ¯ , we find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.

2021 ◽  
Vol 2021 (2) ◽  
Anna Mullin ◽  
Stuart Nicholls ◽  
Holly Pacey ◽  
Michael Parker ◽  
Martin White ◽  

Abstract We present a novel technique for the analysis of proton-proton collision events from the ATLAS and CMS experiments at the Large Hadron Collider. For a given final state and choice of kinematic variables, we build a graph network in which the individual events appear as weighted nodes, with edges between events defined by their distance in kinematic space. We then show that it is possible to calculate local metrics of the network that serve as event-by-event variables for separating signal and background processes, and we evaluate these for a number of different networks that are derived from different distance metrics. Using a supersymmetric electroweakino and stop production as examples, we construct prototype analyses that take account of the fact that the number of simulated Monte Carlo events used in an LHC analysis may differ from the number of events expected in the LHC dataset, allowing an accurate background estimate for a particle search at the LHC to be derived. For the electroweakino example, we show that the use of network variables outperforms both cut-and-count analyses that use the original variables and a boosted decision tree trained on the original variables. The stop example, deliberately chosen to be difficult to exclude due its kinematic similarity with the top background, demonstrates that network variables are not automatically sensitive to BSM physics. Nevertheless, we identify local network metrics that show promise if their robustness under certain assumptions of node-weighted networks can be confirmed.

2021 ◽  
Vol 2021 (2) ◽  
Aranya Bhattacharya ◽  
Anindya Chanda ◽  
Sabyasachi Maulik ◽  
Christian Northe ◽  
Shibaji Roy

Abstract Recently, remarkable progress in recovering the Page curve of an evaporating black hole (BH) in Jackiw-Teitelboim gravity has been achieved through use of Quantum Extremal surfaces (QES). Multi-boundary Wormhole (MbW) models have been crucial in parallel model building in three dimensions. Motivated by this we here use the latter models to compute the subregion complexity of the Hawking quanta of the evaporating BH in AdS3 and obtain the Page curve associated with this information theoretic measure. We use three- and n-boundary wormhole constructions to elucidate our computations of volumes below the Hubeny-Rangamani-Takayanagi (HRT) surfaces at different times. Time is represented by the growing length of the throat horizons corresponding to smaller exits of the multi-boundary wormhole and the evaporating bigger exit shrinks with evolving time. We track the change in choice of HRT surfaces with time and plot the volume with time. The smooth transition of Page curve is realized by a discontinuous jump at Page time in volume subregion complexity plots and the usual Page transition is realized as a phase transition due to the inclusion of the island in this context. We discuss mathematical intricacies and physical insights regarding the inclusion of the extra volume at Page time. The analysis is backed by calculations and lessons from kinematic space and tensor networks.

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