188 research outputs found
A localized approach to generalized Tur\'an problems
Generalized Tur\'an problems ask for the maximum number of copies of a graph
in an -vertex, -free graph, denoted by ex. We show how to
extend the new, localized approach of Brada\v{c}, Malec, and Tompkins to
generalized Tur\'{a}n problems. We weight the copies of (typically taking
), instead of the edges, based on the size of the largest clique, path,
or star containing the vertices of the copy of , and in each case prove a
tight upper bound on the sum of the weights. A consequence of our new localized
theorems is an asymptotic determination of ex for every
having at least one dominating vertex and mex for every
having at least two dominating vertices.Comment: 25 page
The -visibility Localization Game
We study a variant of the Localization game in which the cops have limited
visibility, along with the corresponding optimization parameter, the
-visibility localization number , where is a non-negative
integer. We give bounds on -visibility localization numbers related to
domination, maximum degree, and isoperimetric inequalities. For all , we
give a family of trees with unbounded values. Extending results known
for the localization number, we show that for , every tree contains a
subdivision with . For many , we give the exact value of
for the Cartesian grid graphs, with the remaining cases
being one of two values as long as is sufficiently large. These examples
also illustrate that for all distinct choices of and
$j.
Voxel-wise comparisons of cellular microstructure and diffusion-MRI in mouse hippocampus using 3D Bridging of Optically-clear histology with Neuroimaging Data (3D-BOND)
A key challenge in medical imaging is determining a precise correspondence between image properties and tissue microstructure. This comparison is hindered by disparate scales and resolutions between medical imaging and histology. We present a new technique, 3D Bridging of Optically-clear histology with Neuroimaging Data (3D-BOND), for registering medical images with 3D histology to overcome these limitations. Ex vivo 120 × 120 × 200 μm resolution diffusion-MRI (dMRI) data was acquired at 7 T from adult C57Bl/6 mouse hippocampus. Tissue was then optically cleared using CLARITY and stained with cellular markers and confocal microscopy used to produce high-resolution images of the 3D-tissue microstructure. For each sample, a dense array of hippocampal landmarks was used to drive registration between upsampled dMRI data and the corresponding confocal images. The cell population in each MRI voxel was determined within hippocampal subregions and compared to MRI-derived metrics. 3D-BOND provided robust voxel-wise, cellular correlates of dMRI data. CA1 pyramidal and dentate gyrus granular layers had significantly different mean diffusivity (p > 0.001), which was related to microstructural features. Overall, mean and radial diffusivity correlated with cell and axon density and fractional anisotropy with astrocyte density, while apparent fibre density correlated negatively with axon density. Astrocytes, axons and blood vessels correlated to tensor orientation
Yukawa Unification and the Superpartner Mass Scale
Naturalness in supersymmetry (SUSY) is under siege by increasingly stringent
LHC constraints, but natural electroweak symmetry breaking still remains the
most powerful motivation for superpartner masses within experimental reach. If
naturalness is the wrong criterion then what determines the mass scale of the
superpartners? We motivate supersymmetry by (1) gauge coupling unification, (2)
dark matter, and (3) precision b-tau Yukawa unification. We show that for an
LSP that is a bino-Higgsino admixture, these three requirements lead to an
upper-bound on the stop and sbottom masses in the several TeV regime because
the threshold correction to the bottom mass at the superpartner scale is
required to have a particular size. For tan beta about 50, which is needed for
t-b-tau unification, the stops must be lighter than 2.8 TeV when A_t has the
opposite sign of the gluino mass, as is favored by renormalization group
scaling. For lower values of tan beta, the top and bottom squarks must be even
lighter. Yukawa unification plus dark matter implies that superpartners are
likely in reach of the LHC, after the upgrade to 14 (or 13) TeV, independent of
any considerations of naturalness. We present a model-independent, bottom-up
analysis of the SUSY parameter space that is simultaneously consistent with
Yukawa unification and the hint for m_h = 125 GeV. We study the flavor and dark
matter phenomenology that accompanies this Yukawa unification. A large portion
of the parameter space predicts that the branching fraction for B_s to mu^+
mu^- will be observed to be significantly lower than the SM value.Comment: 34 pages plus appendices, 20 figure
The s ---> d gamma decay in and beyond the Standard Model
The New Physics sensitivity of the s ---> d gamma transition and its
accessibility through hadronic processes are thoroughly investigated. Firstly,
the Standard Model predictions for the direct CP-violating observables in
radiative K decays are systematically improved. Besides, the magnetic
contribution to epsilon prime is estimated and found subleading, even in the
presence of New Physics, and a new strategy to resolve its electroweak versus
QCD penguin fraction is identified. Secondly, the signatures of a series of New
Physics scenarios, characterized as model-independently as possible in terms of
their underlying dynamics, are investigated by combining the information from
all the FCNC transitions in the s ---> d sector.Comment: 54 pages, 14 eps figure
Strong interface-induced spin-orbit coupling in graphene on WS2
Interfacial interactions allow the electronic properties of graphene to be
modified, as recently demonstrated by the appearance of satellite Dirac cones
in the band structure of graphene on hexagonal boron nitride (hBN) substrates.
Ongoing research strives to explore interfacial interactions in a broader class
of materials in order to engineer targeted electronic properties. Here we show
that at an interface with a tungsten disulfide (WS2) substrate, the strength of
the spin-orbit interaction (SOI) in graphene is very strongly enhanced. The
induced SOI leads to a pronounced low-temperature weak anti-localization (WAL)
effect, from which we determine the spin-relaxation time. We find that
spin-relaxation time in graphene is two-to-three orders of magnitude smaller on
WS2 than on SiO2 or hBN, and that it is comparable to the intervalley
scattering time. To interpret our findings we have performed first-principle
electronic structure calculations, which both confirm that carriers in
graphene-on-WS2 experience a strong SOI and allow us to extract a
spin-dependent low-energy effective Hamiltonian. Our analysis further shows
that the use of WS2 substrates opens a possible new route to access topological
states of matter in graphene-based systems.Comment: Originally submitted version in compliance with editorial guidelines.
Final version with expanded discussion of the relation between theory and
experiments to be published in Nature Communication
The neural correlates of dreaming.
Consciousness never fades during waking. However, when awakened from sleep, we sometimes recall dreams and sometimes recall no experiences. Traditionally, dreaming has been identified with rapid eye-movement (REM) sleep, characterized by wake-like, globally 'activated', high-frequency electroencephalographic activity. However, dreaming also occurs in non-REM (NREM) sleep, characterized by prominent low-frequency activity. This challenges our understanding of the neural correlates of conscious experiences in sleep. Using high-density electroencephalography, we contrasted the presence and absence of dreaming in NREM and REM sleep. In both NREM and REM sleep, reports of dream experience were associated with local decreases in low-frequency activity in posterior cortical regions. High-frequency activity in these regions correlated with specific dream contents. Monitoring this posterior 'hot zone' in real time predicted whether an individual reported dreaming or the absence of dream experiences during NREM sleep, suggesting that it may constitute a core correlate of conscious experiences in sleep
Predicting Spike Occurrence and Neuronal Responsiveness from LFPs in Primary Somatosensory Cortex
Local Field Potentials (LFPs) integrate multiple neuronal events like synaptic inputs and intracellular potentials. LFP spatiotemporal features are particularly relevant in view of their applications both in research (e.g. for understanding brain rhythms, inter-areal neural communication and neronal coding) and in the clinics (e.g. for improving invasive Brain-Machine Interface devices). However the relation between LFPs and spikes is complex and not fully understood. As spikes represent the fundamental currency of neuronal communication this gap in knowledge strongly limits our comprehension of neuronal phenomena underlying LFPs. We investigated the LFP-spike relation during tactile stimulation in primary somatosensory (S-I) cortex in the rat. First we quantified how reliably LFPs and spikes code for a stimulus occurrence. Then we used the information obtained from our analyses to design a predictive model for spike occurrence based on LFP inputs. The model was endowed with a flexible meta-structure whose exact form, both in parameters and structure, was estimated by using a multi-objective optimization strategy. Our method provided a set of nonlinear simple equations that maximized the match between models and true neurons in terms of spike timings and Peri Stimulus Time Histograms. We found that both LFPs and spikes can code for stimulus occurrence with millisecond precision, showing, however, high variability. Spike patterns were predicted significantly above chance for 75% of the neurons analysed. Crucially, the level of prediction accuracy depended on the reliability in coding for the stimulus occurrence. The best predictions were obtained when both spikes and LFPs were highly responsive to the stimuli. Spike reliability is known to depend on neuron intrinsic properties (i.e. on channel noise) and on spontaneous local network fluctuations. Our results suggest that the latter, measured through the LFP response variability, play a dominant role
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