Consider a decay process for Trillium-D where at time t = 0 there are y(0) = N grams of Trillium-D. • The rate that Trillium-D decays is proportional to the square root of the mass in grams. • At t = 0, y(0) = 900 grams • Att = 3000 years, y(3000) = 0.5y(0) (a) Find the first-order homogeneous ODE that describes the relationship between

duces a state-of-the-art privacy technique – differential privacy – to the IR community. The purpose of this tutorial is to provide necessary background knowledge for IR researchers to solve the privacy issues in their related research. Differential privacy is a theoretical framework that requires good mathematical skills and Naïve Private FSM ID 100 200 300 400 500 Record a c d b c d a b c e d d b a dc Database D Seq unc {a}{b}{c}{d}p. 3 3 4 4 {e} 1C 1: cand 1-seqs noise 0.2-0.4 0.4-0.5 0.8 Sequence {a }{a c}{a d}{c a}  G. Barthe, B. Köpf, F. Olmedo, and S. Zanella Béguelin, “Probabilistic relational reasoning for differential privacy,” in Proceedings of the 39th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, ser. POPL ’12. Write a differential equation for the amount of chemicals in the pond at any given time. I try to first conceptualize the problem by writing the following equation: $$\text{The amount of chemicals in the pound (in gallons)}=1,000,000 \text{ gallons}-\text{The number of gallons of water in the pond}$$

## Consider a decay process for Trillium-D where at time t = 0 there are y(0) = N grams of Trillium-D. • The rate that Trillium-D decays is proportional to the square root of the mass in grams. • At t = 0, y(0) = 900 grams • Att = 3000 years, y(3000) = 0.5y(0) (a) Find the first-order homogeneous ODE that describes the relationship between

a) (2 Points) Derive an ordinary differential equation describing the amount of chemical over time. b) (0.5 Points) Determine the order of the differential equation derived in part a). c) (1 Point) Is the differential equation derived in part a) linear or nonlinear? Prove your statement. I don't know whether that achieves the comparison you want, as the actual distribution of n-grams is not according to any mathematically tractable function. For instance, letter-trigram distribution is a good way to differentiate the language in use: English, French, Spanish, German, Romanian, etc. have readily differential distributions.

### A differential privacy system on the client device can comprise a privacy budget for each classification of new words. If there is privacy budget available for the classification, then one or more new terms in a classification can be sent to new term learning server, and the privacy budget for the classification reduced.

Naïve Private FSM ID 100 200 300 400 500 Record a c d b c d a b c e d d b a dc Database D Seq unc {a}{b}{c}{d}p. 3 3 4 4 {e} 1C 1: cand 1-seqs noise 0.2-0.4 0.4-0.5 0.8 Sequence {a }{a c}{a d}{c a}  G. Barthe, B. Köpf, F. Olmedo, and S. Zanella Béguelin, “Probabilistic relational reasoning for differential privacy,” in Proceedings of the 39th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, ser. POPL ’12. Write a differential equation for the amount of chemicals in the pond at any given time. I try to first conceptualize the problem by writing the following equation: $$\text{The amount of chemicals in the pound (in gallons)}=1,000,000 \text{ gallons}-\text{The number of gallons of water in the pond}$$ on word n-grams have been observed to perform comparably to more complex CNN and LSTM model architectures for hate speech detection . Using our protocols, Bob can label Alice’s texts as hateful or not without learning which words occur in Alice’s texts, and Alice does not learn which Enabling medical research with differential privacy: the project team includes biomedical researchers from the Genome Institute of Singapore and from NUHS/NUS, along with data mining and security experts from ADSC, I2R, and NTU. The overall plan was for the biomedical researchers to identify the types of analyses where they most wanted to be