Mouhssine Rifaki | Search arXiv

arXiv2026

One Residual with Three Reuses: A Wristband Front End for Gesture Sensing

Continuous wrist-worn hand sensing for gesture interfaces and motor symptom monitoring needs an always-on front end that fits inside a coin-cell power budget while pairing a micro-electro-mechanical-systems (MEMS) inertial measurement unit (IMU) with a 60 GHz frequency-modulated continuous-wave (FMCW) radar to stay robust under occlusion and on-body drift. We present a design study of such a wristband front end in which classifier wake-up gating, mmWave versus IMU routing, and innovation-based EKF measurement reweighting share a single on-chip residual generator. The shared generator occupies 14.4 KB of program memory and 278 B of state and runs at 110K multiply-accumulates (MACs) per frame on an Ambiq Apollo4 Blue Plus class edge microcontroller unit (MCU). Across four public sensor data corpora (IPN Hand, SHREC 2021, MiliPoint 60 GHz FMCW radar, EAT-Radar) the front end reaches detection probability $P_D = 0.72/0.80$ at a 1% false-alarm rate, sustains a 47% classifier invocation energy reduction at 90% gesture detection recall, and lowers pose tracking root-mean-square error by $4.6\times$ under measurement bias drift relative to an adaptive Kalman with $R$-inflation baseline. Measured silicon power and on-body capture are deferred to follow-on hardware; the contribution here is a design study.

cs.LG↗

arXiv2026

Absence of critical scaling in the Schelling segregation model

We find no evidence of critical scaling in the Schelling segregation model, in either the Moore neighborhood or its dense-spectrum extension to Chebyshev radii up to $r_0 = 6$ ($k = 168$ neighbors). On periodic grids up to $L = 320$ with 50 trials per point (> 12,500 runs), every finite-size scaling diagnostic in the Moore baseline fails: the per-$L$ $T_c$ does not drift, Var$(S) \sim L^{-2.02 \pm 0.09}$ matches trivial averaging, $γ/ν\approx 0$, and the scaling collapse never reaches a finite optimum. The 8-site Moore neighborhood restricts satisfaction to ratios $j/k$ with $k \leq 8$, giving $S(T)$ a staircase structure with 23 rational thresholds; discreteness alone does not forbid criticality (cf. the Ising model), but the scaling evidence rules it out empirically. A branching-ratio calculation predicts subcritical cascades of mean size $1/(1-R)$ and is validated by perturbation experiments to within 15%; the multiscalar dissimilarity length stays finite across the transition. The dense-spectrum extension strengthens the negative verdict: across $r_0 \in {3,4,5,6}$ on $L \in {40,80,160}$ the Binder cumulant has no $L$-curve crossing and the per-$L$ $T_c$ drift is monotonic and unsaturated; at $r_0 = 4$, extending to $L = 320$ gives $α= -2.70$, below the critical boundary $α= -2$, dissolving an apparent $α= +0.81$ signal visible only on $L \in {40,80}$. The mechanism is the absence of long-range correlation in equilibrium plus deterministic high-$k$ dynamics, not the staircase structure. With a Beta-distributed heterogeneous tolerance, the intolerant tail drives segregation even at moderate population-average tolerance. The staircase theorem and cascade mechanism together account for the Schelling transition without invoking critical phenomena.

cond-mat.stat-mech↗