Banking regulations set minimum levels of capital for banks. These requirements are generally formulated through a ratio of capital to risk-weighted assets. A risk-weighting scheme assigns a weight to each asset or category of assets and effectively functions as a linear constraint on a bank’s portfolio choice; it also changes the incentives for banks to hold various kinds of assets. In this pa...

The papers [25], [20], [1], [9], [12], [10], [22], [3], [15], [2], [23], [19], [26], [24], [27], [21], [8], [18], [5], [11], [6], [17], [16], [4], [14], and [7] provide the terminology and notation for this paper. In this article we present several logical schemes. The scheme UparrowUnion deals with a relational structure A and a unary predicate P, and states that: Let S be a family of subsets ...

For the cyclic group G = Z/nZ and any non-empty A ∈ Z. We define the Davenport constant of G with weight A, denoted by DA(n), to be the least natural number k such that for any sequence (x1, · · · , xk) with xi ∈ G, there exists a non-empty subsequence (xj1, · · · , xjl) and a1, · · · , al ∈ A such that ∑l i=1 aixji = 0. Similarly, we define the constant EA(n) to be the least t ∈ N such that fo...

We'll recall (again) some definitions from last time: Definition 1 (Database Update Sequence) Let D ∈ N |X | be any database and let Using the exponential mechanism as a distinguisher, we proved the following utility theorem about the IC mechanism: Theorem 3 Given a B(α)-DUA, the Iterative Construction mechanism is (α, β) accurate and-differentially private for: α ≥ 8B(α/2) nn log C γ and (, δ)...

The well-known Lawvere category [0,∞] of extended real positive numbers comes with a monoidal closed structure where the tensor product is the sum. But [0,∞] has another such structure, given by multiplication, which is *-autonomous and a CL-algebra (linked with classical linear logic). Normed sets, with a norm in [0,∞], inherit thus two symmetric monoidal closed structures, and categories enri...