Whole-field visual motion drives swimming in larval zebrafish via a stochastic process

Caudo-rostral whole-field visual motion elicits forward locomotion in many organisms, including larval zebrafish. Here, we investigate the dependence on the latency to initiate this forward swimming as a function of the speed of the visual motion. We show that latency is highly dependent on speed for slow speeds ( 1.5 s, which is much longer than neuronal transduction processes. What mechanisms underlie these long latencies? We propose two alternative, biologically inspired models that could account for this latency to initiate swimming: an integrate and fire model, which is history dependent, and a stochastic Poisson model, which has no history dependence. We use these models to predict the behavior of larvae when presented with whole-field motion of varying speed and find that the stochastic process shows better agreement with the experimental data. Finally, we discuss possible neuronal implementations of these models

The Structure and Timescales of Heat Perception in Larval Zebrafish

SummaryAvoiding temperatures outside the physiological range is critical for animal survival, but how temperature dynamics are transformed into behavioral output is largely not understood. Here, we used an infrared laser to challenge freely swimming larval zebrafish with “white noise” heat stimuli and built quantitative models relating external sensory information and internal state to behavioral output. These models revealed that larval zebrafish integrate temperature information over a time-window of 400 ms preceding a swim bout and that swimming is suppressed right after the end of a bout. Our results suggest that larval zebrafish compute both an integral and a derivative across heat in time to guide their next movement. Our models put important constraints on the type of computations that occur in the nervous system and reveal principles of how somatosensory temperature information is processed to guide behavioral decisions such as sensitivity to both absolute levels and changes in stimulation

On the vanishing of negative K-groups

Let k be an infinite perfect field of positive characteristic p and assume that strong resolution of singularities holds over k. We prove that, if X is a d-dimensional noetherian scheme whose underlying reduced scheme is essentially of finite type over the field k, then the negative K-group K_q(X) vanishes for every q < -d. This partially affirms a conjecture of Weibel.Comment: Math. Ann. (to appear

Periodicity of hermitian K-groups

Bott periodicity for the unitary, orthogonal and symplectic groups is fundamental to topological K-theory. Analogous to unitary topological K-theory, for algebraic K-groups with finite coefficients similar periodicity results are consequences of the Milnor and Bloch-Kato conjectures, affirmed by Voevodsky, Rost and others. More generally, we prove that periodicity of the algebraic K-groups for any ring implies periodicity for its hermitian K-groups, analogous to orthogonal and symplectic topological K-theory. The proofs use in an essential way higher KSC theories extending those of Anderson and Green. They also provide an upper bound for the higher hermitian K-groups in terms of the higher algebraic K-groups. We also relate periodicity to etale hermitian K-groups by proving ahermitian version of Thomason's etale descent theorem. The results are illustrated in detail for local fields, rings of integers in number fields, smooth complex algebraic varieties, rings of continuous functions on compact spaces, and group rings

Cohomological Hasse principle and motivic cohomology for arithmetic schemes

In 1985 Kazuya Kato formulated a fascinating framework of conjectures which generalizes the Hasse principle for the Brauer group of a global field to the so-called cohomological Hasse principle for an arithmetic scheme. In this paper we prove the prime-to-characteristic part of the cohomological Hasse principle. We also explain its implications on finiteness of motivic cohomology and special values of zeta functions.Comment: 47 pages, final versio

Techniques, Computations, and Conjectures for Semi-Topological K-Theory

We establish the existence of an &quot;Atiyah-Hirzebruch-like&quot; spectral sequence relating the morphic cohomology groups of a smooth, quasi-projective complex variety to its semi-topological K-groups. This spectral sequence is compatible with (and, indeed, is built from) the motivic spectral sequence that connects the motivic cohomology and algebraic K-theory of varieties, and it is also compatible with the classical Atiyah-Hirzebruch spectral sequence in algebraic topology

K-THEORY OF CONES OF SMOOTH VARIETIES

Abstract. Let R be the homogeneous coordinate ring of a smooth projective variety X over a field k of characteristic 0. We calculate the K-theory of R in terms of the geometry of the projective embedding of X. In particular, if X is a curve then we calculate K0(R) and K1(R), and prove that K−1(R) = ⊕H 1 (C, O(n)). The formula for K0(R) involves the Zariski cohomology of twisted Kähler differentials on the variety. Let R = k ⊕R1 ⊕ · · · be the homogeneous coordinate ring of a smooth projective variety X over a field k of characteristic 0. In this paper we compute the lower K-theory (Ki(R), i ≤ 1) in terms of the Zariski cohomology groups H ∗ (X, O(t)) and H ∗ (X, Ω ∗ X (t)), where O(1) is the ample line bundle of the embedding and Ω ∗ X denotes the Kähler differentials of X relative to Q. We also obtain computations of the higher K-groups Kn(R)/Kn(k), especially for curves. A complete calculation for the conic xy = z 2 is given in Theorem 4.3. These calculations have become possible thanks to the new techniques introduced in [1], [2] and [4]. Here, for example, is part of Theorem 2.1; R + is the seminormalization of R. Theorem. Let R be the homogeneous coordinate ring of a smooth d-dimensional projective variety X in P N k. Then Pic(R) ∼ = (R + /R) and K0(R) ∼ = Z ⊕ Pic(R) ⊕ ⊕d i=