Single-Symbol ML Decodable Distributed STBCs for Partially-Coherent Cooperative Networks

Space-time block codes (STBCs) that are single-symbol decodable (SSD) in a co-located multiple antenna setting need not be SSD in a distributed cooperative communication setting. A relay network with N relays and a single source-destination pair is called a partially-coherent relay channel (PCRC) if the destination has perfect channel state information (CSI) of all the channels and the relays have only the phase information of the source-to-relay channels. In this paper, first, a new set of necessary and sufficient conditions for a STBC to be SSD for co-located multiple antenna communication is obtained. Then, this is extended to a set of necessary and sufficient conditions for a distributed STBC (DSTBC) to be SSD for a PCRC, by identifying the additional conditions. Using this, several SSD DSTBCs for PCRC are identified among the known classes of STBCs. It is proved that even if a SSD STBC for a co-located MIMO channel does not satisfy the additional conditions for the code to be SSD for a PCRC, single-symbol decoding of it in a PCRC gives full-diversity and only coding gain is lost. It is shown that when a DSTBC is SSD for a PCRC, then arbitrary coordinate interleaving of the in-phase and quadrature-phase components of the variables does not disturb its SSD property for PCRC. Finally, it is shown that the possibility of {\em channel phase compensation} operation at the relay nodes using partial CSI at the relays increases the possible rate of SSD DSTBCs from $\frac{2}{N}$ when the relays do not have CSI to 1/2, which is independent of N

Virtual equivariant Grothendieck-Riemann-Roch formula

For a G-scheme X with a given equivariant perfect obstruction theory, we prove a virtual equivariant Grothendieck-Riemann-Roch formula, this is an extension of a result of \textit{B. Fantechi} and \textit{L. Göttsche} [Geom. Topol. 14, No. 1, 83--115 (2010; Zbl 1194.14017)] to the equivariant context. We also prove a virtual non-abelian localization theorem for schemes over C with proper actions

Asymptotic distributions of Periodically Driven Stochastic Systems

We study the large-time behaviour of Brownian particles moving through a viscous medium in a confined potential, and which are further subjected to position-dependent driving forces that are periodic in time. We focus on the case where these driving forces are rapidly oscillating with an amplitude that is not necessarily small. We develop a perturbative method for the high-frequency regime to find the large-time behavior of periodically driven stochastic systems. The asymptotic distribution of Brownian particles is then determined to second order. To first order, these particles are found to execute small-amplitude oscillations around an effective static potential which can have interesting forms.Comment: 8 pages; Included an e.g. in the last section; added references; final version in two column

Oscillating states of driven Langevin systems in large viscous regime

We employ an appropriate perturbative scheme in the large viscous regime to study oscillating states in driven Langevin systems. We explicitly determine oscillating state distribution of under-damped Brownian particle subjected to thermal, viscous and potential drives to linear order in anharmonic perturbation. We also evaluate various non-equilibrium observables relevant to characterize the oscillating states. We find that the effects of viscous drive on oscillating states are measurable even in the leading order and show that the thermodynamic properties of the system in these states are immensely distinct from those in equilibrium.Comment: 14 pages, 2 figure

Critical dynamics of nonconserved NN-vector model with anisotropic nonequilibrium perturbations

We study dynamic field theories for nonconserving $N$-vector models that are subject to spatial-anisotropic bias perturbations. We first investigate the conditions under which these field theories can have a single length scale. When N=2 or $N \ge 4$, it turns out that there are no such field theories, and, hence, the corresponding models are pushed by the bias into the Ising class. We further construct nontrivial field theories for N=3 case with certain bias perturbations and analyze the renormalization-group flow equations. We find that the three-component systems can exhibit rich critical behavior belonging to two different universality classes.Comment: Included RG analysis and discussion on new universality classe

Implications of z>∼12z>{\sim}12 JWST galaxies for galaxy formation at high redshift

Using a semi-analytic galaxy-formation model, we study analogues of 8 recently discovered JWST galaxies at $z>{\sim}12$. We select analogues from a cosmological simulation with a $(311{\rm cMpc})^3$ volume and an effective particle number of $10^{12}$ enabling resolution of every atomic-cooling galaxy at $z{\le}20$. We vary model parameters to reproduce the observed UV luminosity function of $5{<}z{<}13$, aiming for a statistically representative high-redshift galaxy mock catalogue. Using the forward-modelled JWST photometry, we identify analogues from this catalogue and study their properties as well as possible evolutionary paths and local environments. We find faint JWST galaxies ($M_{\rm UV}>{\sim}-19.5$) remain consistent with standard galaxy-formation model and that our fiducial catalogue includes large samples of their analogues. The properties of these analogues broadly agree with conventional SED fitting results, except for having systematically lower redshifts due to the evolving UV luminosity function, and for having higher specific star formation rates as a result of burstier histories in our model. On the other hand, only a handful of bright galaxy analogues can be identified for observed $z{\sim}12$ galaxies. Moreover, in order to reproduce $z>{\sim}16$ JWST galaxy candidates, boosted star-forming efficiencies and reduced feedback regulation are necessary relative to models of lower-redshift populations. This suggests star formation in the first galaxies could differ significantly from their lower-redshift counterparts. We also find that these candidates are subject to low-redshift contamination, which is present in our fiducial results as both the dusty or quiescent galaxies at $z{\sim}5$.Comment: 10 pages, 11 figures, submitted to MNRAS, comments welcome