VC-Dimension of Hyperplanes over Finite Fields

Let $\mathbb{F}_q^d$ be the $d$-dimensional vector space over the finite field with $q$ elements. For a subset $E\subseteq \mathbb{F}_q^d$ and a fixed nonzero $t\in \mathbb{F}_q$, let $\mathcal{H}_t(E)=\{h_y: y\in E\}$, where $h_y$ is the indicator function of the set $\{x\in E: x\cdot y=t\}$. Two of the authors, with Maxwell Sun, showed in the case $d=3$ that if $|E|\geq Cq^{\frac{11}{4}}$ and $q$ is sufficiently large, then the VC-dimension of $\mathcal{H}_t(E)$ is 3. In this paper, we generalize the result to arbitrary dimension and improve the exponent in the case $d=3$.Comment: 9 pages, 1 figur

Inside-Out Corporate Governance

Until late in the twentieth century, internal corporate governance—that is, decision making by the principal constituencies of the firm—was clearly distinct from outside oversight by regulators, auditors and credit rating agencies, and markets. With the 1980s takeover wave and hedge funds’ and equity funds’ more recent involvement in corporate governance, the distinction between inside and outside governance has eroded. The tools of inside governance are now routinely employed by governance outsiders, intertwining the two traditional modes of governance. We argue in this Article that the shift has created a new governance paradigm, which we call inside-out corporate governance. Using the inside-out model as our lens, and drawing on comparisons to Italian and E.U. governance, we explore three areas of corporate governance that have been pervasively restructured by the Dodd-Frank Act and subsequent regulation: proxy access, credit rating agencies, and derivatives. We begin, in Part I, with proxy access, arguing that the new scheme for minority shareholder access excludes the very outsiders it ostensibly integrates into corporate governance. In Part II, which focuses on auditing and credit rating agencies, we argue that the inside-out relationship—in which the corporation itself chooses its gatekeeper—is deeply problematic but cannot be “cured.” The most realistic strategy is to create more flexibility in the audit relationship, and diminish the importance of credit ratings. Part III analyzes the new derivatives regulation. Here, we argue that Congress’s effort to sharply separate the inside and outside uses of derivatives is incoherent from a corporate governance perspective. We conclude by briefly speculating about the future implications of inside-out governance

Inside-Out Corporate Governance

Until late in the twentieth century, internal corporate governance—that is, decision making by the principal constituencies of the firm—was clearly distinct from outside oversight by regulators, auditors and credit rating agencies, and markets. With the 1980s takeover wave and hedge funds’ and equity funds’ more recent involvement in corporate governance, the distinction between inside and outside governance has eroded. The tools of inside governance are now routinely employed by governance outsiders, intertwining the two traditional modes of governance. We argue in this Article that the shift has created a new governance paradigm, which we call inside-out corporate governance. Using the inside-out model as our lens, and drawing on comparisons to Italian and E.U. governance, we explore three areas of corporate governance that have been pervasively restructured by the Dodd-Frank Act and subsequent regulation: proxy access, credit rating agencies, and derivatives. We begin, in Part I, with proxy access, arguing that the new scheme for minority shareholder access excludes the very outsiders it ostensibly integrates into corporate governance. In Part II, which focuses on auditing and credit rating agencies, we argue that the inside-out relationship—in which the corporation itself chooses its gatekeeper—is deeply problematic but cannot be “cured.” The most realistic strategy is to create more flexibility in the audit relationship, and diminish the importance of credit ratings. Part III analyzes the new derivatives regulation. Here, we argue that Congress’s effort to sharply separate the inside and outside uses of derivatives is incoherent from a corporate governance perspective. We conclude by briefly speculating about the future implications of inside-out governance

Dallas Museum of Fashion Collection

Evening ensemble of golden olive green lightweight wool twill: A) Short jacket. No collar, center front opening with 4 hook-and-loop closures. Back has section of bloused fabric giving the effect of a faux hood hanging back. Wide bands of decoration on front, yoke, and on faux "hood" of back, in the form of golden vines of gold braid and leaves and flowers of gold and pearl beads. Fully lined in olive silk crepe. Label at center back inside neckline: "Milgrim". B) Full length evening dress of matching fabric. Sleeveless, wide straps. Moderate neckline with "bow" effect at front. Just below knot of bow is accent of brown mink. Slight train to back of skirt. Side zipper closure. Fully lined in green silk crepe matching jacket. Label inside skirt: "Milgrim" C) Muff of matching fabric. Large trapezoidal shaped muff, the front with two large tiers of mink tails and a large bow with floral pattern in tiny white seed beads accented in gold beads and with scrolling gold embroidery. Zipper compartment on back. Label inside pocket: "This Article / 10 Year Guarantee" "Berlou / Moth / Proofed

An overlooked problem in Turkish-Russian relations : the 1878 War indemnity

Donated by Klaus KreiserReprinted from in : International Journal of Middle East Studies, Vol: 9, No: 4, 1978

Study Collection, Westheimer Research Gallery

Cloche style hat in taupe felt. Slightly flared brim. Trimmed at front with red feather bird. Green and black coque feathers drape from front over back of hat. Beige colored veil on front. Elastic band for securing hat to wearer's head. Designer's label on inside hatband: "Milgrim

Body Talk

The primary focus of this research is to enrich my perspective as a playwright by gathering data on the topic of body-shame. Dr. Mello and I are conducting interviews with people of varying genders, ages, and walks of life in order to discover how each person experiences body-shame and body-ease. I will write a draft of a play which will prove to be richer and more truthful with the aid of this new data. That will then be workshopped and performed with a company in Helsinki, a city with a lasting tradition of theater that strongly impacts public discourse

Charlene Milgrim interview

Charlene Milgrim talks about the beauty of the Oakland campus and how her education at CCAC was the foundation for all her future work