Direct Systems of Spherical Functions and Representations

Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional symmetric spaces $G_\infty/K_\infty = \varinjlim G_n/K_n$. We use the representation theoretic construction $\phi (x) =$ where $e$ is a $K_\infty$--fixed unit vector for $\pi$. Specifically, we look at representations $\pi_\infty = \varinjlim \pi_n$ of $G_\infty$ where $\pi_n$ is $K_n$--spherical, so the spherical representations $\pi_n$ and the corresponding spherical functions $\phi_n$ are related by $\phi_n(x) = <e_n, \pi_n(x)e_n>$ where $e_n$ is a $K_n$--fixed unit vector for $\pi_n$, and we consider the possibility of constructing a $K_\infty$--spherical function $\phi_\infty = \lim \phi_n$. We settle that matter by proving the equivalence of condtions (i) $\{e_n\}$ converges to a nonzero $K_\infty$--fixed vector $e$, and (ii) $G_\infty/K_\infty$ has finite symmetric space rank (equivalently, it is the Grassmann manifold of $p$--planes in \F^\infty where $p < \infty$ and \F is $\R$, \C or \H). In that finite rank case we also prove the functional equation $\phi(x)\phi(y) = \lim_{n\to \infty} \int_{K_n}\phi(xky)dk$ of Faraut and Olshanskii, which is their definition of spherical functions.Comment: 17 pages. New material added on the finite rank case

Defectors cannot be detected during"small talk" with strangers.

To account for the widespread human tendency to cooperate in one-shot social dilemmas, some theorists have proposed that cooperators can be reliably detected based on ethological displays that are difficult to fake. Experimental findings have supported the view that cooperators can be distinguished from defectors based on "thin slices" of behavior, but the relevant cues have remained elusive, and the role of the judge's perspective remains unclear. In this study, we followed triadic conversations among unacquainted same-sex college students with unannounced dyadic one-shot prisoner's dilemmas, and asked participants to guess the PD decisions made toward them and among the other two participants. Two other sets of participants guessed the PD decisions after viewing videotape of the conversations, either with foreknowledge (informed), or without foreknowledge (naïve), of the post-conversation PD. Only naïve video viewers approached better-than-chance prediction accuracy, and they were significantly accurate at predicting the PD decisions of only opposite-sexed conversation participants. Four ethological displays recently proposed to cue defection in one-shot social dilemmas (arms crossed, lean back, hand touch, and face touch) failed to predict either actual defection or guesses of defection by any category of observer. Our results cast doubt on the role of "greenbeard" signals in the evolution of human prosociality, although they suggest that eavesdropping may be more informative about others' cooperative propensities than direct interaction

Treatment of failed articular cartilage reconstructive procedures of the knee: A systematic review

Background: Symptomatic articular cartilage lesions of the knee are common and are being treated surgically with increasing frequency. While many studies have reported outcomes following a variety of cartilage restoration procedures, few have investigated outcomes of revision surgery after a failed attempt at cartilage repair or reconstruction. Purpose: To investigate outcomes of revision cartilage restoration procedures for symptomatic articular cartilage lesions of the knee following a previously failed cartilage reconstructive procedure. Study Design: Systematic review; Level of evidence, 4. Methods: A literature search was performed by use of the PubMed, EMBASE, and MEDLINE/Ovid databases for relevant articles published between 1975 and 2017 that evaluated patients undergoing revision cartilage restoration procedure(s) and reported outcomes using validated outcome measures. For studies meeting inclusion criteria, relevant information was extracted. Results: Ten studies met the inclusion criteria. Lesions most commonly occurred in the medial femoral condyle (MFC) (52.8%), with marrow stimulation techniques (MST) the index procedure most frequently performed (70.7%). Three studies demonstrated inferior outcomes of autologous chondrocyte implantation (ACI) following a previous failed cartilage procedure compared with primary ACI. One study comparing osteochondral allograft (OCA) transplant following failed microfracture (MFX) with primary OCA transplant demonstrated similar clinical outcomes and graft survival at midterm follow-up. No studies reported outcomes following osteochondral autograft transfer (OAT) or newer techniques. Conclusion: This systematic review of the literature reporting outcomes following revision articular cartilage restoration procedures (most commonly involving the MFC) demonstrated a high proportion of patients who underwent prior MST. Evidence is sufficient to suggest that caution should be taken in performing ACI in the setting of prior MST, likely secondary to subchondral bone compromise. OCA appears to be a good revision treatment option even if the subchondral bone has been violated from prior surgery or fracture. </jats:sec

Ultrafast switching of photonic entanglement

To deploy and operate a quantum network which utilizes existing telecommunications infrastructure, it is necessary to be able to route entangled photons at high speeds, with minimal loss and signal-band noise, and---most importantly---without disturbing the photons' quantum state. Here we present a switch which fulfills these requirements and characterize its performance at the single photon level; it exhibits a 200-ps switching window, a 120:1 contrast ratio, 1.5 dB loss, and induces no measurable degradation in the switched photons' entangled-state fidelity (< 0.002). Furthermore, because this type of switch couples the temporal and spatial degrees of freedom, it provides an important new tool with which to encode multiple-qubit states in a single photon. As a proof-of-principle demonstration of this capability, we demultiplex a single quantum channel from a dual-channel, time-division-multiplexed entangled photon stream, effectively performing a controlled-bit-flip on a two-qubit subspace of a five-qubit, two-photon state

Real-time decoding of question-and-answer speech dialogue using human cortical activity.

Natural communication often occurs in dialogue, differentially engaging auditory and sensorimotor brain regions during listening and speaking. However, previous attempts to decode speech directly from the human brain typically consider listening or speaking tasks in isolation. Here, human participants listened to questions and responded aloud with answers while we used high-density electrocorticography (ECoG) recordings to detect when they heard or said an utterance and to then decode the utterance's identity. Because certain answers were only plausible responses to certain questions, we could dynamically update the prior probabilities of each answer using the decoded question likelihoods as context. We decode produced and perceived utterances with accuracy rates as high as 61% and 76%, respectively (chance is 7% and 20%). Contextual integration of decoded question likelihoods significantly improves answer decoding. These results demonstrate real-time decoding of speech in an interactive, conversational setting, which has important implications for patients who are unable to communicate

State Dependence of Stimulus-Induced Variability Tuning in Macaque MT

Behavioral states marked by varying levels of arousal and attention modulate some properties of cortical responses (e.g. average firing rates or pairwise correlations), yet it is not fully understood what drives these response changes and how they might affect downstream stimulus decoding. Here we show that changes in state modulate the tuning of response variance-to-mean ratios (Fano factors) in a fashion that is neither predicted by a Poisson spiking model nor changes in the mean firing rate, with a substantial effect on stimulus discriminability. We recorded motion-sensitive neurons in middle temporal cortex (MT) in two states: alert fixation and light, opioid anesthesia. Anesthesia tended to lower average spike counts, without decreasing trial-to-trial variability compared to the alert state. Under anesthesia, within-trial fluctuations in excitability were correlated over longer time scales compared to the alert state, creating supra-Poisson Fano factors. In contrast, alert-state MT neurons have higher mean firing rates and largely sub-Poisson variability that is stimulus-dependent and cannot be explained by firing rate differences alone. The absence of such stimulus-induced variability tuning in the anesthetized state suggests different sources of variability between states. A simple model explains state-dependent shifts in the distribution of observed Fano factors via a suppression in the variance of gain fluctuations in the alert state. A population model with stimulus-induced variability tuning and behaviorally constrained information-limiting correlations explores the potential enhancement in stimulus discriminability by the cortical population in the alert state.Comment: 36 pages, 18 figure